1. My brain told me, for whatever reason, that Infinity is both equal and opposite to Zero, and gave me the image of an eternally expanding circle, where 0 is the starting point, and infinity is the ending point... which are the same point on the circle (as a curved line rather than a plane... so the inner part of the circle is non-existent).

It was also suggested that x/0 tends toward Infinity, and x/Infinity tends toward Zero. That x(Infinity) is meaningless (it equals infinity), x(0) is meaningless (it equals zero), that 0/0 is 1. That Infinity/Infinity is 1, and that 0 trumps Infinity. 0(Infinity) = 0, 0/Infinity = 0.

Typing Infinity so many times is causing infinity to lose meaning like a continuous sense becomes dulled. If I keep typing it, Infinity will become so dulled as to be nothing (zero).

I'm inclined to believe it, but I can't really pinpoint why.

What are your thoughts on Infinity is equal and opposite to Zero?

(Not interested in your thoughts as to why I am inclined to listen to the weird shit my brain tells me, or anything other than Infinity and Zero).

2.

3. Are you stoned?

4. Originally Posted by Beer w/Straw
Are you stoned?
That is totally a question that falls into the last sentence of my post =P

No, I am not stoned, lol... I also wasn't stoned when this series of thoughts drifted through my brain meats.

5. Allow me to take a look at your thoughts.

Originally Posted by Velexia
My brain told me, for whatever reason, that Infinity is both equal and opposite to Zero, and gave me the image of an eternally expanding circle, where 0 is the starting point, and infinity is the ending point... which are the same point on the circle (as a curved line rather than a plane... so the inner part of the circle is non-existent).

A few remarks here:
1. The concept of infinity is a confusing one and I will not pretend that I grasp all the details about this concept. However, I do know that infinity is not a number, thus how can it be equal (and opposite to 0)?

2. Imagine a circle with a radius of 1 meter and its centre on (0,0) in a x,y-coordinate system. What position is the starting point? What if the radius becomes 2 meter?

It was also suggested that x/0 tends toward Infinity, and x/Infinity tends toward Zero. That x(Infinity) is meaningless (it equals infinity), x(0) is meaningless (it equals zero), that 0/0 is 1. That Infinity/Infinity is 1, and that 0 trumps Infinity. 0(Infinity) = 0, 0/Infinity = 0.

You make the mistake by treating infinity as an number. It is not.

Furthermore, 0/0 != 1. It is undefined.
Same goes for Inf/Inf.

Typing Infinity so many times is causing infinity to lose meaning like a continuous sense becomes dulled. If I keep typing it, Infinity will become so dulled as to be nothing (zero). I'm inclined to believe it, but I can't really pinpoint why.

I do not share your belief. I cannot accept your thoughts due to the errors.

6. Originally Posted by Velexia
My brain told me, for whatever reason, that Infinity is both equal and opposite to Zero ...
There have been a great many threads on this in the past. Most of these have been created by people who have little or no understanding of math. So I am kinda surprised to see the same comments from someone who has, apparently, studied math to a reasonable level. You obviously know that infinity is defined as being greater than any number; it is hard to see how this can be equated to zero, the smallest (non-negative) number.

And which infinity do you consider to be equal to zero?

That x(Infinity) is meaningless (it equals infinity), x(0) is meaningless (it equals zero)
I'm not quite sure what the notation x(infinity) and x(0) are supposed to mean. But if the results are infinity and 0 then they are not meaningless.

0/0 is 1
You can reach that conclusion using limits. But you can equally well get any other result, which is why division by zero is said to be undefined.

7. Originally Posted by Cogito Ergo Sum
Allow me to take a look at your thoughts.

Originally Posted by Velexia
My brain told me, for whatever reason, that Infinity is both equal and opposite to Zero, and gave me the image of an eternally expanding circle, where 0 is the starting point, and infinity is the ending point... which are the same point on the circle (as a curved line rather than a plane... so the inner part of the circle is non-existent).

A few remarks here:
1. The concept of infinity is a confusing one and I will not pretend that I grasp all the details about this concept. However, I do know that infinity is not a number, thus how can it be equal (and opposite to 0)?

2. Imagine a circle with a radius of 1 meter and its centre on (0,0) in a x,y-coordinate system. What position is the starting point? What if the radius becomes 2 meter?

It was also suggested that x/0 tends toward Infinity, and x/Infinity tends toward Zero. That x(Infinity) is meaningless (it equals infinity), x(0) is meaningless (it equals zero), that 0/0 is 1. That Infinity/Infinity is 1, and that 0 trumps Infinity. 0(Infinity) = 0, 0/Infinity = 0.

You make the mistake by treating infinity as an number. It is not.

Furthermore, 0/0 != 1. It is undefined.
Same goes for Inf/Inf.

Typing Infinity so many times is causing infinity to lose meaning like a continuous sense becomes dulled. If I keep typing it, Infinity will become so dulled as to be nothing (zero). I'm inclined to believe it, but I can't really pinpoint why.

I do not share your belief. I cannot accept your thoughts due to the errors.
Well, I don't really imagine infinity as a number, more like a progression. Hence the image of the ever expanding circle on which these two points lie.

0/0 != 1. It is undefined. --- is true from a dogmatic mathematical standpoint. It's undefined because no one gave it any definition, because the concept makes no sense (except to that weird corner of my brain). Also, this is not in the math section for pretty much that exact reason =3

The errors are concepts of a mathematical system which does not define them... so... I mean... It's not that I am going to tear down the foundations of math, because that shit is rock solid... but you can't say it's invalid simply because it's not defined.

This is sadly somewhat akin to trying to argue the existence of God, believe me, I know, and blegh to that. I'm just sharing weird thoughts, and I thank you for your input in the matter =)

For your [2.] In the perspective I was imagining, the 0/Infinity was placed at (0,0) and as it expanded it did so only in two quadrants. So the start and endpoints remained the same. Really the whole circle bit is just a representation of the infinite number of reference points between 0 and infinity, progressing from 0 into infinity... since infinity is, a progression, and not a number.

Infinity cannot really take place in standard mathematics because of it's very nature.... but still there are some minor applications where it can be valid. Such as x/infinity where I am essentially restructuring whatever value we set equal to x/infinity approaches 0 in x/y as y approaches infinity...

But anyway... brains do weird shit sometimes. Mine likes to toy with this idea. I would never dare to try to make a mathematical proof out of this.

8. Originally Posted by Strange
Originally Posted by Velexia
My brain told me, for whatever reason, that Infinity is both equal and opposite to Zero ...
There have been a great many threads on this in the past. Most of these have been created by people who have little or no understanding of math. So I am kinda surprised to see the same comments from someone who has, apparently, studied math to a reasonable level. You obviously know that infinity is defined as being greater than any number; it is hard to see how this can be equated to zero, the smallest (non-negative) number.

And which infinity do you consider to be equal to zero?

That x(Infinity) is meaningless (it equals infinity), x(0) is meaningless (it equals zero)
I'm not quite sure what the notation x(infinity) and x(0) are supposed to mean. But if the results are infinity and 0 then they are not meaningless.

0/0 is 1
You can reach that conclusion using limits. But you can equally well get any other result, which is why division by zero is said to be undefined.

That was in reference to multiplication x(0) etc... in that multiplying anything with these two has no effect. Granted, they have applications in math... so they are not meaningless in all regards, but I simply meant that they cause no change. Communication can be hard <_<

I am pretty sure I left out some brain thread where 0/0 was also equal to 0, or anything really... This is why it's left undefined in math. It squirms about and as far as I can recall has no practical application.

9. There was this other silly notion of rather than thinking of a negative number as 0 minus some quantity, say, 5, being -5.

-5 is actually a representation of Infinity minus 5. That's probably where the equal and opposite idea really came from... sort of a flipside mirror idea.

Going from infinity to zero is just as much a process as zero to infinity... (you have to assume here that you are somewhat tethered to one or the other so that as infinity progresses along, you are pulled with it... or maybe the direct opposite side of the circle (or midpoint of the line between the two) is progressing outward toward both equally so if you place one at an end and the other at a beginning, and then just continuously expand the relative "distance" between them...

10. Originally Posted by Velexia
Well, I don't really imagine infinity as a number, more like a progression. Hence the image of the ever expanding circle on which these two points lie.

How can the concept of infinity be a progression?

0/0 != 1. It is undefined. --- is true from a dogmatic mathematical standpoint. It's undefined because no one gave it any definition, because the concept makes no sense (except to that weird corner of my brain). Also, this is not in the math section for pretty much that exact reason =3

0/0 is undefined because it does not have a definite number of solutions. At least, that is how I learned it.
I have no idea why you use the term "dogmatic mathematical standpoint".

The errors are concepts of a mathematical system which does not define them... so... I mean... It's not that I am going to tear down the foundations of math, because that shit is rock solid... but you can't say it's invalid simply because it's not defined.

I did not state that.

For your [2.] In the perspective I was imagining, the 0/Infinity was placed at (0,0) and as it expanded it did so only in two quadrants. So the start and endpoints remained the same. Really the whole circle bit is just a representation of the infinite number of reference points between 0 and infinity, progressing from 0 into infinity... since infinity is, a progression, and not a number.

I am afraid I do not understand your representation.

Infinity cannot really take place in standard mathematics because of it's very nature.... but still there are some minor applications where it can be valid. Such as x/infinity where I am essentially restructuring whatever value we set equal to x/infinity approaches 0 in x/y as y approaches infinity...

You left me more confused than I already was, to be honest.

11. I term infinity a progression in the sense that if you were to attempt to describe infinity, you might say it is a series of numbers that continues on forever. So, progressing from 1 you go to 2..3...4..5..6..7.. etc.. a progression ad infinitum. I can't imagine infinity as a thing that exists complete and intact instantaneously, because to me that would cause it to have a definite end.

Granted, in my circle and description of infinity I gave infinity a definite end, but really all I did was abuse the name infinity by assuming that as a progression it has a "front" which is the thing continuing... attached that to a fixed point, and transfered the real infinity to the opposite side of the circle... that midpoint between beginning and end, and gave it no name or definition, merely an existence and definite effect which creates infinity. Madness. Granted it could be the entire line connecting beginning and end that creates the expansion of the circle into infinity all the same. This rabbit hole...

I know you didn't state that, but I wasn't addressing your version of the circle because it did not seem to lead anywhere that related to the circle I had in my mind, so I tried to describe that circle of mine better.

Sorry to confuse, I meant to describe a limit with that last one.

12. Originally Posted by Velexia
I term infinity a progression in the sense that if you were to attempt to describe infinity, you might say it is a series of numbers that continues on forever.
Isn't that a definition of the natural numbers? That sequence never leads to infinity.

Infinity is formally defined, and not as a progression.

13. Originally Posted by Strange
Originally Posted by Velexia
I term infinity a progression in the sense that if you were to attempt to describe infinity, you might say it is a series of numbers that continues on forever.
Isn't that a definition of the natural numbers? That sequence never leads to infinity.

Infinity is formally defined, and not as a progression.
I suppose it wouldn't lead to infinity unless we continuously supplied words with which to describe ever larger numbers... So the concept of an endless progression seems to fall perfectly within the realm of the formal definition. I think we're starting to get into semantics here =P

14. Infinity isn't a real number.

x/0 where x doesn't equal 0 is complex infinity.

0/0 is indeterminate.

15. Hi, welcome =3

16. Originally Posted by Velexia
I suppose it wouldn't lead to infinity unless we continuously supplied words with which to describe ever larger numbers...
The whole point is that while you can continue to add words to describe ever bigger numbers (or use the successor function) then you will never reach infinity. Because you can always add 1 to create a larger number. Therefore you will never reach infinity.

I think we're starting to get into semantics here =P
It seems like a reasonably good informal equivalent to the formal definition of the natural numbers.

17. Originally Posted by Beer w/Straw
Infinity isn't a real number.
What do you mean by real number?

A member of the set of reals? In which case, you are right.

Or something we can define mathematical operations on? In which case you are wrong.

18. Originally Posted by Strange
Originally Posted by Velexia
I suppose it wouldn't lead to infinity unless we continuously supplied words with which to describe ever larger numbers...
The whole point is that while you can continue to add words to describe ever bigger numbers (or use the successor function) then you will never reach infinity. Because you can always add 1 to create a larger number. Therefore you will never reach infinity.

I think we're starting to get into semantics here =P
It seems like a reasonably good informal equivalent to the formal definition of the natural numbers.
Buuuut, infinity is not a thing that can be reached... That's in it's very nature...

19. Originally Posted by Velexia
Buuuut, infinity is not a thing that can be reached... That's in it's very nature...
I don't know what "reached" means. Do you "reach" 100 or 1036? No, you just use the numbers.

The same applies to infinity (or, more accurately, infinities).

20. Imagine it in terms of limits... "as x approaches infinity" x can never "reach" infinity, but it can most definitely approach it. Generally, most things that can be approached, can be reached. Except infinity. Zero can be reached, and approached.

21. Originally Posted by Velexia
Imagine it in terms of limits... "as x approaches infinity" x can never "reach" infinity, but it can most definitely approach it. Generally, most things that can be approached, can be reached. Except infinity.
Infinity, and the mathematical operators on it, can be defined in the same way as any other numbers. There is no need to "reach" anything.

And in the mathematics of limits, you can "reach" infinity just as much as you can "reach" 0 or 42.

22. (Not interested in your thoughts as to why I am inclined to listen to the weird shit my brain tells me, or anything other than Infinity and Zero).
I think you doth protest too much.

Georg Cantor was the first mathematician to present a rigorous and logically consistent treatment of infinite sets; Georg Cantor - Wikipedia, the free encyclopedia
Cantor illuminated different sizes of infinity; Countable set - Wikipedia, the free encyclopedia, and; Uncountable set - Wikipedia, the free encyclopedia
And here is Cantors argument to this effect; Cantor's diagonal argument - Wikipedia, the free encyclopedia

23. infinity is every thing and zero is nothing.

24. Originally Posted by GiantEvil
(Not interested in your thoughts as to why I am inclined to listen to the weird shit my brain tells me, or anything other than Infinity and Zero).
I think you doth protest too much.

Georg Cantor was the first mathematician to present a rigorous and logically consistent treatment of infinite sets; Georg Cantor - Wikipedia, the free encyclopedia
Cantor illuminated different sizes of infinity; Countable set - Wikipedia, the free encyclopedia, and; Uncountable set - Wikipedia, the free encyclopedia
And here is Cantors argument to this effect; Cantor's diagonal argument - Wikipedia, the free encyclopedia
The internet doth make me cautious of people inclined to do nothing more than inflame <_<

It's kind of a disclaimer of the sort "I know this is crazy talk, but I think it's semi-interesting, let's not talk about how it's crazy talk, because talk about talk is boring to me."

I remember this guy (well his writing, let's not get literal here, heh). It's a good read ~_^

25. Just to be pedantic here, infinity in standard real analysis (limits, calculus) is different to infinity in set theory (ordinals, cardinals) and its best to try keep the concepts seperate in your mind else heaps of confusion can result. They encode different ideas entirely, one of something increasing without bound, one about ordering types and another about the relative size of sets.

26. Back to zero and infinity. Wouldn't infinity be the invert of zero, both being opposite sides of an extreme. Or, would they extend in the relative zero direction past zero and into negative numbers having a positive and negative infinities equalling infinity with the zero possibly as infinity over two.

27. Originally Posted by Hill Billy Holmes
Back to zero and infinity. Wouldn't infinity be the invert of zero, both being opposite sides of an extreme. Or, would they extend in the relative zero direction past zero and into negative numbers having a positive and negative infinities equalling infinity with the zero possibly as infinity over two.
I have no idea what any of that is supposed to mean

28. Originally Posted by river_rat
I have no idea what any of that is supposed to mean
That was one of his more coherent and lucid posts.

The odds are that if it were comprehensible, it would be wrong.

29. Originally Posted by Hill Billy Holmes
Back to zero and infinity. Wouldn't infinity be the invert of zero, both being opposite sides of an extreme. Or, would they extend in the relative zero direction past zero and into negative numbers having a positive and negative infinities equalling infinity with the zero possibly as infinity over two.
The idea was that going past zero into negative was actually starting at this endpoint that is now erroneously still holding the artifact of the name infinity, and going toward zero from the complete opposite end. A diagram of this image in my mind would probably help a lot.

30. Here's a very ghetto paint version I just put together.

X = Psuedo-infinity
0 = Zero

Psuedo-infinity is the equal and opposite of zero; a number, quantity, thing, or idea that increases as the circle expands (the arrows symbolize this), but can't ever be assigned a specific value.

The idea being that the circle expands in such a way as to contain all numbers (natural, rational, irrational, integer, etc) along the curved line.

31. Originally Posted by Velexia
Psuedo-infinity is the equal and opposite of zero; a number, quantity, thing, or idea that increases as the circle expands (the arrows symbolize this), but can't ever be assigned a specific value.
The idea being that the circle expands in such a way as to contain all numbers (natural, rational, irrational, integer, etc) along the curved line.
None of the dimensions were infinite in length.

Originally Posted by Velexia
a number, quantity, thing, or idea
Perhaps your lack of specificity is indicative of the accuracy of your claims.

32. Originally Posted by RedPanda
None of the dimensions were infinite in length.
You might have to use your imagination.

Also:
Originally Posted by Velexia
idea that increases as the circle expands (the arrows symbolize this), but can't ever be assigned a specific value.

The idea being that the circle expands in such a way as to contain all numbers (natural, rational, irrational, integer, etc) along the curved line.
Originally Posted by RedPanda
Originally Posted by Velexia
a number, quantity, thing, or idea
Perhaps your lack of specificity is indicative of the accuracy of your claims.
I'm not sure I am making any real claims here <_<

Also, that was not a lack of specificity, similar to "such a way as to contain all numbers (natural, rational, irrational, integer, etc)" not being a lack of specificity.

33. Originally Posted by Velexia
You might have to use your imagination.
No thanks. I'd rather not use the "make shit up" technique that you are so adept at.

Originally Posted by Velexia
I'm not sure I am making any real claims here <_<
Apart from this obvious claim:
"Psuedo-infinity is the equal and opposite of zero; a number, quantity, thing, or idea that increases as the circle expands (the arrows symbolize this), but can't ever be assigned a specific value."

Granted - it is not a real claim, in the sense that it is complete bollocks.

Originally Posted by Velexia
Also, that was not a lack of specificity, similar to "such a way as to contain all numbers (natural, rational, irrational, integer, etc)" not being a lack of specificity.
Using the word 'thing' indicates a complete lack of specificity - that is what the word 'thing' is for.

Personally, I don't think you've even driven passed a college.

34. You realize this is the philosophy section, not the math section, right? And I did say "(Not interested in your thoughts as to why I am inclined to listen to the weird shit my brain tells me, or anything other than Infinity and Zero). "

Psuedo-infinity is a word I just concocted for myself, so it would make sense that I should define something I just made up on the spot, so people have any idea of what I mean when I say it.

Now, why don't you stop trying to provoke me, throughout the whole forum. Also, be aware of this:

Originally Posted by John Galt
Moderator Warning: Here's the deal.

1. Velexia, your posting style is provocative and much of what you say is thought to be ill-informed by several members. Do not react to anything you construe as a personal remark.

2. Other members: before this situation becomes more out of hand than it is, right now stop making anything that could be construed as a personal remark about Velexia.

Anyone, including members of the mod-team, including myself, who ignores this warning will be suspended.

Do not respond to this warning in this thread. That will also earn you a suspension.

And thanks to those who have kept their hair on.
Originally Posted by RedPanda
Personally, I don't think you've even driven passed a college.
*past

35. What does mean for your circle? Does the diameter also equal infinity?

You need axioms.

Making up something like "pseudo-infinity" would be against the rules of philosophy.

36. Originally Posted by Velexia
Originally Posted by RedPanda
Personally, I don't think you've even driven passed a college.
*past
Ah yes. It's an adverb, isn't it.
I have given up ever hoping to get that correct.

Personally, I don't think you've even driven past a college.

37. Originally Posted by RedPanda
Originally Posted by Velexia
Originally Posted by RedPanda
Personally, I don't think you've even driven passed a college.
*past
Ah yes. It's an adverb, isn't it.
I have given up ever hoping to get the correct.

Personally, I don't think you've even driven past a college.
That's better.
It was just a jab anyway.

Your opinion of me is not meaningful to the discussion. You were rude in the voicing of your opinion. That's in violation of the rules of this forum. So please. Stop.

38. Originally Posted by Beer w/Straw
Making up something like "pseudo-infinity" would be against the rules of philosophy.
Most people that have had no real experience of philosophy think that philosophy is just "making stuff up".

39. Originally Posted by Beer w/Straw
What does mean for your circle? Does the diameter also equal infinity?

You need axioms.

Making up something like "pseudo-infinity" would be against the rules of philosophy.
I am not familiar with the rules of philosophy I'm afraid.

I think was in the realm of equal to 1...

40. Originally Posted by RedPanda
Originally Posted by Beer w/Straw
Making up something like "pseudo-infinity" would be against the rules of philosophy.
Most people that have had no real experience of philosophy think that philosophy is just "making stuff up".
Philosophy is the study of general and fundamental problems, such as those connected with reality, existence, knowledge, values, reason, mind, and language.[1][2] Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational argument.[3] In more casual speech, by extension, "philosophy" can refer to "the most basic beliefs, concepts, and attitudes of an individual or group".[4]
The word "philosophy" comes from the Ancient Greek φιλοσοφία (philosophia), which literally means "love of wisdom".[5][6][7] The introduction of the terms "philosopher" and "philosophy" has been ascribed to the Greek thinker Pythagoras.[8]

I don't see an implication of rules here (beyond using logic), but I'm willing to listen, and learn =)

41. Originally Posted by Velexia
I think was in the realm of equal to 1...

Inf/Inf is also undefined (and thus not necessarily equal to 1) , as I have stated in post # 4.

42. Originally Posted by Cogito Ergo Sum
Originally Posted by Velexia
I think was in the realm of equal to 1...

Inf/Inf is also undefined (and thus not necessarily equal to 1) , as I have stated in post # 4.
Don't mathematicians use the idea that it is equal to 1, to cancel out infinities that occur in some equations?

I mean, performing these kind of mathematical operations on infinity is... kind of meaningless in most senses.

Conceptually... 2/1 and 1/1 and 1/2 ... I can see as... two parts of one thing, one part of one thing, and one part of two things.

So... in that regard is infinite parts of infinite things. What the hell does that mean?

But then we consider 1/1 = 1, 2/2 = 1, 3/3 = 1... ad infinitum... and that seems to make sense.

43. Originally Posted by Velexia
Don't mathematicians use the idea that is equal to 1, to cancel out infinities that occur in some equations?
I mean, performing these kind of mathematical operations on infinity is... kind of meaningless in most senses.

Not that I am aware of.

I can illustrate with an example that can be 0:

Suppose that f(x) = x * ln(x); if x → +0, then:

f(x) = 0 * ln(0)

We know that ln(0) is equal to -Inf, thus we get:

f(x) = 0 * (-Inf)

This is undefined. To solve this, it is rewritten as an fracture:

f(x) = ln(x) / (1/x)

Given the fact that x → +0, then we approach one divided by zero, which is Inf. Ergo, we get:

f(x) = Inf/Inf

And now the rule of L'Hopital is applied, namely taking the derivative of the numerator and the denominator:

D(x) = (1/x) / (-1/x²)

If this is rewritten, then it yields:

D(x) = (1/x)*(-x²)
D(x) = -x

And because x → +0:

x = 0 and so Inf/Inf = 0

PS: My apologies for the rather non-mathematical notation.

44. Originally Posted by Cogito Ergo Sum

Not that I am aware of.

I can illustrate with an example that Inf/Inf can be 0:

Suppose that f(x) = x * ln(x); if x → +0, then:

f(x) = 0 * ln(0)

We know that ln(0) is equal to -Inf, thus we get:

f(x) = 0 * (-Inf)

This is undefined. To solve this, it is rewritten as an fracture:

f(x) = ln(x) / (1/x)

Given the fact that x → +0, then we approach one divided by zero, which is Inf. Ergo, we get:

f(x) = Inf/Inf

And now the rule of L'Hopital is applied, namely taking the derivative of the numerator and the denominator:

D(x) = (1/x) / (-1/x²)

If this is rewritten, then it yields:

D(x) = (1/x)*(-x²)
D(x) = -x

And because x → +0:

x = 0 and so Inf/Inf = 0

PS: My apologies for the rather non-mathematical notation.
Heh, I can follow that. We have to allow for Ln(0) = -Inf and division by zero, but hey, I've pretty much done crazy rule breaking stuff like that already here.

Can we make equal anything beyond 1 and 0? (Without defining one infinity as greater than or less than another).

45. Originally Posted by Velexia
Heh, I can follow that. We have to allow for Ln(0) = -Inf and division by zero, but hey, I've pretty much done crazy rule breaking stuff like that already here.

It would have been better to state that and that

Yet, these are mathematical operations that are quite common in calculus, especially in calculating limits.

Can we make equal anything beyond 1 and 0? (Without defining one infinity as greater than or less than another).

Of course. It can be :

Suppose that f(x) = x / ²log(x); if x → +Inf, then:

f(x) = +Inf / ²log(+Inf)

And now the rule of L'Hopital is applied (because of the Inf/Inf), namely taking the derivative of the numerator and the denominator:

D(x) = 1 / (1 / (x * ln(2)))

If this is rewritten, then it yields:

D(x) = x * ln(2)

And because x → +Inf:

x = +Inf and so Inf/Inf = +Inf

46. I suspected as much. ~_^

Pretty sure from that, we can also make it equal to 2... and thus, with 0, 1, 2, and Infinity in our toolbelt, we can make equal to any real number.

47. ^tex/tex in square brackets

\Large \frac{\alpha ^e \infty ^{1/\mu }}{\frac{\pi }{e}}\leq \int_{\psi }^{\sigma } \zeta \, d\gamma

:EDIT:

Regardless, however, it makes no sense what I put.

48. Forgive me for my lack of strength in math...

What is alpha referring to...
What is mu referring to...
What are sigma and psi referring to...
what does the following squiggly refer to...
and why is dy so weird lookins =P (what do they refer to?)

Or are you just making some kind of point about nonsense =P

49. It's scribbled nonsense. It merely shows you can use the [tex] command.

50. Nobody in this thread mentioned the Riemann sphere? Zero and infinity are the two opposite poles on a sphere.

Riemann sphere - Wikipedia, the free encyclopedia

51. So what happens when we multiply zero by infinity? Does it become zero or does it become infinite? Which value takes precedence? Does that even make sense as a question?

52. My math teacher in school (who knew math good) said that zero over zero equaled zero "or" one. 1/1=1 unit integer unit, 2/2= 1 integer unit etc/etc= 1 etc unit, 0/0= "1" zero unit "0". I won't define it with calculess, but as I recall it was o or 1 . In my last clueless incomprehenseble post I tried to define 0 as a center point on an infinite line.

53. Oh yes also. I forgot to mention that I really really hate calculus. Not because its so hard ( although that could be a factor) but that it inherently allows for inaccuracy.

You can't use calculus at the grocery checkout, to compute cost of purchase, without getting arrested.

54. Originally Posted by Hill Billy Holmes
In my last clueless incomprehenseble post I tried to define 0 as a center point on an infinite line.
But that's exactly what zero is!

We have the real line, extending infinitely to the left through the negative numbers -1, -2, -1000, etc. And extending infinitely to the right, 1, 2, 3, ... and of course with all the rest of the real numbers as points on the line.

And right there in the middle is zero. Neither negative nor positive. It's the balance point of an infinite line.

I think your visualization is very good. Of course one can quibble that the number 47 is just as good a candidate for the "center point," since every point on the line has infinitely many other points to the right, and infinitely many to the left.

But zero is the only number that is not a negative number and not a positive number. It's in its very own category by itself.

Most people think intuitively of zero as being the midpoint of the real line, technical quibbles notwithstanding. So I agree with you.

56. Originally Posted by Hill Billy Holmes
My math teacher in school (who knew math good) said that zero over zero equaled zero "or" one.
I hate to break this to you, but your maths teacher was wrong - 0/0 is not defined.

57. Anything over anything is one except in the case of zero. Zero can either be 0 or 1. Go back and try logic and reason this time. Zero is a weird unit since it represents apsolute nothing.

58. Originally Posted by Hill Billy Holmes
Zero can either be 0 or 1.
No.

59. Originally Posted by Hill Billy Holmes
Anything over anything is one except in the case of zero. Zero can either be 0 or 1. Go back and try logic and reason this time. Zero is a weird unit since it represents apsolute nothing.
Perhaps I haven't made myself clear enough - in the space of the real numbers ( which is what we are talking about here ) division by zero is not defined, hence 0/0 is not defined. See here :

Division by zero - Wikipedia, the free encyclopedia

60. Originally Posted by Hill Billy Holmes
Zero can either be 0 or 1. Go back and try logic and reason this time.
What nonsense is this ??

61. Perhaps. Then perhaps again use 0/0 in any equation you wish, no matter how complex. Results? Proof!

62. Originally Posted by Hill Billy Holmes
Perhaps.
There is no "perhaps" here. Division by zero is not defined, which is mathematical fact.

63. Don't get emotional, but with proof yes I would be corrected. But my guess is that you're checking in in a book and repeating it. So we are repeating. Use 0/0 in any equation or set of equations you like and check the results.

64. Originally Posted by Hill Billy Holmes
Don't get emotional, but with proof yes I would be corrected. But my guess is that you're checking in in a book and repeating it. So we are repeating. Use 0/0 in any equation or set of equations you like and check the results.
x/x = 1

5x/x = 5

123.456x/x = 123.456

Now substitute x=0 and you can "prove" that 0/0 = any value at all. In other words, it is undefined.

And before you say anything, I didn't look that up in a book. But why some morons seems to think nbooks are evil is beyond me. Apparently, making shit up is more valued than being well informed.

65. Originally Posted by Hill Billy Holmes
Don't get emotional
I think you have had too much eggnog now.

Use 0/0 in any equation or set of equations you like and check the results.
Consider 0/0=a, with some real number a. Now, since any number multiplied by zero yields zero, the term 0/0 cannot have a well defined value. To put this more technically :

but, at the same time

Hence 0/0 is not a well defined expression; such constructs are called indeterminate forms.

66. I am more than corrected. Sorry to put you through the trouble. You have more accurately defined this than my math teacher. Thanks.

67. Originally Posted by Hill Billy Holmes
I am more than corrected. Sorry to put you through the trouble. You have more accurately defined this than my math teacher. Thanks.
No problem

68. Originally Posted by Daecon
So what happens when we multiply zero by infinity? Does it become zero or does it become infinite? Which value takes precedence? Does that even make sense as a question?

That would be undefined, just as .

69. Infinity seems quite problematic for mathematics due to its ambiguity. Mathematics is a language of precision dealing with precise numbers in its application, and then we have infinity which is not a precise number but just the opposite.

70. Originally Posted by van erst
Infinity seems quite problematic for mathematics due to its ambiguity. Mathematics is a language of precision dealing with precise numbers in its application, and then we have infinity which is not a precise number but just the opposite.
Cantor!

71. Originally Posted by Strange
Originally Posted by van erst
Infinity seems quite problematic for mathematics due to its ambiguity. Mathematics is a language of precision dealing with precise numbers in its application, and then we have infinity which is not a precise number but just the opposite.
Cantor!
Yes? (Not implying that I am Georg)

72. A generic question for all.

Would you consider infinity a number (like e.g. 3.14159), only a symbol (like X), or neither?

73. Not a real number.

74. Originally Posted by van erst
Would you consider infinity a number (like e.g. 3.14159), only a symbol (like X), or neither?
It's just a concept indicating "without boundary"; its definitely not a number, but it is of course a symbol.

75. Originally Posted by Beer w/Straw
Not a real number.
Could it be just a symbol not representing any a real number?

76. Originally Posted by Markus Hanke
Originally Posted by van erst
Would you consider infinity a number (like e.g. 3.14159), only a symbol (like X), or neither?
It's just a concept indicating "without boundary"; its definitely not a number, but it is of course a symbol.
So it is a symbol that has different rules than the other symbols?

77. Originally Posted by van erst
So it is a symbol that has different rules than the other symbols?
Well no, it's just a placeholder for a concept. When it comes down to it, all symbols used in mathematics are just placeholders for concepts, and have certain rules associated with them. In this case, it is important to remember though that the concept it refers to is not a number.

78. So it's placeholder that does not fall under the same rules as the other placeholders?

79. Originally Posted by van erst
So it's placeholder that does not fall under the same rules as the other placeholders?
Not sure what you mean by that; if you are asking whether or not it can be treated like a number or a variable, then no. What it does is indicate that something increases without bounds.

80. Originally Posted by Markus Hanke
Originally Posted by van erst
So it's placeholder that does not fall under the same rules as the other placeholders?
Not sure what you mean by that; if you are asking whether or not it can be treated like a number or a variable, then no. What it does is indicate that something increases without bounds.
I'm just poking it with a stick from different aspects..

I suppose the real world representation of infinite would be the Universe as the totality of all existence. In reality nothing can be added to the Universe as it already has everything that exists within its scope. So deriving from reality it seems that nothing can be added to infinity.

81. Originally Posted by van erst
I suppose the real world representation of infinite would be the Universe as the totality of all existence.
We don't know whether or not the universe is infinite. Infinity is a slippery slope - consider for example the geometric object in my avatar. It is called a Menger cube. Its sides have a well defined length, yet its surface area is infinite, and it encloses precisely zero volume...

82. Originally Posted by Markus Hanke
Originally Posted by van erst
I suppose the real world representation of infinite would be the Universe as the totality of all existence.
We don't know whether or not the universe is infinite. Infinity is a slippery slope - consider for example the geometric object in my avatar. It is called a Menger cube. Its sides have a well defined length, yet its surface area is infinite, and it encloses precisely zero volume...
How can we know that the surface area of the Menger cube is infinite?

83. Originally Posted by van erst
How can we know that the surface area of the Menger cube is infinite?
It can be calculated. I should mention that the Menger cube is not a real, physical object, but a mathematical construct from fractal geometry. See here : Menger sponge - Wikipedia, the free encyclopedia

84. Originally Posted by Markus Hanke
Originally Posted by van erst
How can we know that the surface area of the Menger cube is infinite?
It can be calculated. I should mention that the Menger cube is not a real, physical object, but a mathematical construct from fractal geometry. See here : Menger sponge - Wikipedia, the free encyclopedia
It seems that the surface area of the cube would actually approach a specific numeric ratio of the side of the cube. If you perform iterations, each new cubic hole subtracts from the previous surface area. The added surface area approaches 0.

85. Originally Posted by van erst
The added surface area approaches 0.
Actually this might not be correct and the added area actually approaches infinity. So yes the surface area of the cube would be infinite. Elusive little thing this one, do not approach when feeling tired .

Perhaps something similar mathematical proof of infinity of the Universe could be found.

86. Infinity = Zero ?
is it based on position . not sure .
if infinity = zero , then even infinity / 2 = zero , infinity / (infinity- 1) =0 ,
Infinity - infinity = not necessary to be zero .
zero is initial to one , final to - 1.
Infinite is initial to ?
final to ?
if final , then no infiniteness

87. Originally Posted by sciencestudy
Infinity = Zero ?
No.

zero is initial to one , final to - 1.
Huh ?

if final , then no infiniteness

88. Originally Posted by Markus Hanke
Originally Posted by Hill Billy Holmes
Perhaps.
There is no "perhaps" here. Division by zero is not defined, which is mathematical convention.
Something was broken, I fixed it though.

89. Originally Posted by someguy1
Nobody in this thread mentioned the Riemann sphere? Zero and infinity are the two opposite poles on a sphere.

Riemann sphere - Wikipedia, the free encyclopedia
That's pretty interesting, it seems to share a lot in common with my.. 1... or 2... dimensional concept. A much more advanced version =)

90. Originally Posted by Strange
Originally Posted by Hill Billy Holmes
Don't get emotional, but with proof yes I would be corrected. But my guess is that you're checking in in a book and repeating it. So we are repeating. Use 0/0 in any equation or set of equations you like and check the results.
x/x = 1

5x/x = 5

123.456x/x = 123.456

Now substitute x=0 and you can "prove" that 0/0 = any value at all. In other words, it is undefined.

And before you say anything, I didn't look that up in a book. But why some morons seems to think nbooks are evil is beyond me. Apparently, making shit up is more valued than being well informed.
That is poor logic.

(0)/(0) = 0.
5(0)/(0) = 0.
123.456(0)/(0) = 0.

We could also just write undefined. But from the very start you are making all of the numerators equal to zero.

It's not about books being evil. Anyone can mimic, repeat from a book. Using logic to come to conclusions is more valuable. We can divide people into two sorts: The kind that see something written in a book and accept it (or are told something by someone), and the kind that think it through themselves either before or after reading about / being told of a subject (or of course, experiencing for themselves).

91. Originally Posted by Markus Hanke
Originally Posted by van erst
How can we know that the surface area of the Menger cube is infinite?
It can be calculated. I should mention that the Menger cube is not a real, physical object, but a mathematical construct from fractal geometry. See here : Menger sponge - Wikipedia, the free encyclopedia
I love Fractals <3

I have yet to formally take a class on Fractal Geometry, but I feel I really need to, because, man, I love fractals.

92. Originally Posted by Velexia
Something was broken, I fixed it though.
It's mathematical fact because 0/0 is an indeterminate form - proof to be found in post #64.

93. Originally Posted by sciencestudy
Infinity = Zero ?
is it based on position . not sure .
if infinity = zero , then even infinity / 2 = zero , infinity / (infinity- 1) =0 ,
Infinity - infinity = not necessary to be zero .
zero is initial to one , final to - 1.
Infinite is initial to ?
final to ?
if final , then no infiniteness

I get what you are saying, which is where I came up with the concept that this "infinity at a point" (opposite zero, thus final at 1, initial at -1) is more a pseudo infinity... the real infinity is within the curve itself... as the distance between 0 and the psuedo-infinity along the curve of the circle is ever expanding to accommodate, well, infinity.

94. Originally Posted by Markus Hanke
Originally Posted by Velexia
Something was broken, I fixed it though.
It's mathematical fact because 0/0 is an indeterminate form - proof to be found in post #64.
Fact: something that actually exists; reality; truth.

Convention: a rule, method, or practice established by usage; custom.

I stand firm.

95. Originally Posted by Velexia
I stand firm.
You can stand in whichever way you like - 0/0 still remains an indeterminate form, and hence undefined, which is a fact.

96. Originally Posted by Markus Hanke
Originally Posted by sciencestudy
Infinity = Zero ?
No.

zero is initial to one , final to - 1.
Huh ?

if final , then no infiniteness
I must say this brightened my day nicely. In this context those eyes make me laugh and I can not stop

Perhaps the set of conclusions needs some more clarification

97. Strange in Post #5 had a sort of good definition. For any number x, (x+)=i, For any number x, (x-x)=0 .Books are static like still pictures. Mind is more of a laptop with moving pictures and bright colors. More romantic.

98. Originally Posted by Markus Hanke
Originally Posted by Velexia
I stand firm.
You can stand in whichever way you like - 0/0 still remains an indeterminate form, and hence undefined, which is a fact.
The fact is, in math, it is undefined. Which is a convention. See, this is why talking to you is pointless.

99. Originally Posted by Velexia
That is poor logic.
More a simplification of the argument using limits, for the benefit of the math-impaired (e.g. HBH).

(0)/(0) = 0.
5(0)/(0) = 0.
123.456(0)/(0) = 0.
Now that is poor logic. Begging the question, to be specific.

We could also just write undefined. But from the very start you are making all of the numerators equal to zero.

It's not about books being evil. Anyone can mimic, repeat from a book. Using logic to come to conclusions is more valuable. We can divide people into two sorts: The kind that see something written in a book and accept it (or are told something by someone), and the kind that think it through themselves either before or after reading about / being told of a subject (or of course, experiencing for themselves).
There is no real difference between those, to my mind. They are both open minded and willing to learn. They just take slightly different routes.

You're missing the third sort (which seem to be common in science forums): those who think that any information from a book is worthless "because you are just repeating it"; while something you make up is valuable, no matter how wrong or nonsensical it is, "because it demonstrates creativity". Those are the morons, I referred to.

100. Originally Posted by Hill Billy Holmes
Strange in Post #5 had a sort of good definition. For any number x, (x+)=i, For any number x, (x-x)=0 .Books are static like still pictures. Mind is more of a laptop with moving pictures and bright colors. More romantic.
I would prefer my name were not associated with that gibberish.

101. Originally Posted by Strange
Originally Posted by Velexia
(0)/(0) = 0.
5(0)/(0) = 0.
123.456(0)/(0) = 0.
Now that is poor logic. Begging the question, to be specific.
You multiply all terms in the numerator, until you have one number, before dividing. That number, is zero. The only begging around here is you begging me to call you stupid.

Originally Posted by Strange
It's not about books being evil. Anyone can mimic, repeat from a book. Using logic to come to conclusions is more valuable. We can divide people into two sorts: The kind that see something written in a book and accept it (or are told something by someone), and the kind that think it through themselves either before or after reading about / being told of a subject (or of course, experiencing for themselves).
There is no real difference between those, to my mind. They are both open minded and willing to learn. They just take slightly different routes.
It goes to the very core, I see.

Originally Posted by Strange
You're missing the third sort (which seem to be common in science forums): those who think that any information from a book is worthless "because you are just repeating it"; while something you make up is valuable, no matter how wrong or nonsensical it is, "because it demonstrates creativity". Those are the morons, I referred to.
That's a valid point, they don't quite fit in either category.

Page 1 of 2 12 Last
 Bookmarks
##### Bookmarks
 Posting Permissions
 You may not post new threads You may not post replies You may not post attachments You may not edit your posts   BB code is On Smilies are On [IMG] code is On [VIDEO] code is On HTML code is Off Trackbacks are Off Pingbacks are Off Refbacks are On Terms of Use Agreement