# Thread: Is infinity equal to negative infinity?

1. If we make this a number line:

<------------------------->

then infinity and negative infinity would be at

negative infinity<-----------------------------> infinity

Now, infinity is believed to be 1/0

And negative infinity is -1/0

*****

0 is both negative and positive, so both quantities must be the same, right? This means that infinity and negative infinity are the same.

The simple way of disproving this is to find a function f(x) that approaches some number at infinity, and another number at negative infinity. If any function approaches two different numbers at this point, then my premise would be disproved.

If negative infinity is equal to infinity, then I assume that the number line would be an infinitely narrow ellipse where infinity and negative infinity are the two endpoints. Would this be a new way of approaching limits?

I haven't done calculus yet.

2.

3. Here's a function that disproves your idea, like you said.

The limit as x goes to infinity is 1 and the limit as x goes to negative infinity is -1.

4. Originally Posted by Duelix
If we make this a number line:

<------------------------->

then infinity and negative infinity would be at

negative infinity<-----------------------------> infinity

Now, infinity is believed to be 1/0

And negative infinity is -1/0

*****

0 is both negative and positive, so both quantities must be the same, right? This means that infinity and negative infinity are the same.

The simple way of disproving this is to find a function f(x) that approaches some number at infinity, and another number at negative infinity. If any function approaches two different numbers at this point, then my premise would be disproved.

If negative infinity is equal to infinity, then I assume that the number line would be an infinitely narrow ellipse where infinity and negative infinity are the two endpoints. Would this be a new way of approaching limits?

I haven't done calculus yet.
Neither infinity nor negative infinity are really numbers.

There are various ways to handle the concept of infinity, which you can see discussed in the thread here:

http://www.thescienceforum.com/What-...ity-23750t.php

There is another meaning that is suggested by your question. You can adjoint a single number to the real line, the "point at infinity" and create a compactification of the line, which in this case is simply a circle. The" point at infinity" being used to tie the "ends" of the line together. This is sometimes called the real projective line, or the one-point compactification of the line.

http://en.wikipedia.org/wiki/Real_projective_line

You can also adjoint two point to the line -- positive infinity and negative infinity -- and compactify it in that manner. That is what is discussed in the thread noted above.

It is not true that 1/0 is infinity. In fact 1/0 is not defined at all.

5. where is if c is positive, and if c is negative. The function, as dr rocket pointed out above, has no meaning when x is 0.

6. Originally Posted by Duelix
If we make this a number line:
0 is both negative and positive, so both quantities must be the same, right? This means that infinity and negative infinity are the same.
0 isn't negative and isn't positive. 0 is 0.

7. Originally Posted by Yuliana
Originally Posted by Duelix
If we make this a number line:
0 is both negative and positive, so both quantities must be the same, right? This means that infinity and negative infinity are the same.
0 isn't negative and isn't positive. 0 is 0.
no, really :wink:

8. 1-19-13 Duelix....what if I were to tell you that there are two different infinities that I have been looking into? Here is one: I use pizzas as models since the pizza is representative of a whole and its parts. One pizza can be expressed as10 to the zero power. I ask you, what exponential power would ten pizzas have? Would it be 10 to the first power? What exponential power would 100 hundred pizzas have? Can the number of 100 pizzas be expressed as 10 to the 2nd power?

The next question is
: do I have enough concrete materials and ingredients to make an infinite number pizzas? The next question: what exponential power would you give an infinite number of pizzas?
Or do I have enough materials and ingredients to make only a finite number of pizzas up to 10 to the "positive z? Can you express an infinite number of pizzas as exponent: 10 to the positive infinity....let me know if you want to talk about more concepts of infinity! eaglepass: my quote-IN ORDER TO THINK OUTSIDE THE BOX, YOU MUST FIRST STEP OUT OF THE BOX!

9. Originally Posted by eaglepass
IN ORDER TO THINK OUTSIDE THE BOX, YOU MUST FIRST STEP OUT OF THE BOX!
This box?
c1454_pizza_box.jpg
I agree.

10. Note the artist's powerful use of colour. This far more than just a rejection of convention as it may, at first, appear. It is highly symbolic at multiple levels. First, note that the colour chosen is red. This colour appeals to our most basic instincts. It is a powerful colour. It is the first pigment that early man had access to. In contrast to blue, which was for millennia the rarest and then the first synthetic pigment. Red is also the first colour word that a language gains. It is also the colour of blood. In this case, dried blood. The blood of ideas that have been dead for three years.

But at another, epistemological, level the artists is making us think about how the message is presented. He takes McLuhan's famous dictum, "the medium is the message" and drags at once to the dawn of man and into the 21st century. Should we see patterns in the use of red throughout the message? Do the highlighted words contain a second level of meaning? We can spend hours working on this puzzle. But then we realise he has pulled of a brilliant double bluff: neither the message nor the medium have any meaning at all.

And then we come to his final line, present on all his work almost like a signature, where he attempts throw the blame for the lack of meaning onto the viewer.

Truly one of his most important works.

[From Empty Boxes; New Perspectives on Modern Art by Francis Arkwright and Fanny Adams, published by Sanguedolce Press, 2013]

11. A case for an infinitely large cosmos (universe) can be made. But can there be an infinitely small cosmos (universe)? ...

12. Originally Posted by Strange
Note the artist's powerful use of colour.
The artist's work in ceramics is legendary.

13. Originally Posted by Write4U
A case for an infinitely large cosmos (universe) can be made. But can there be an infinitely small cosmos (universe)? ...
An infinitely large possibility is a possibility. There seem to be good indications for a lower limit on size (Planck dimension, loop quantum gravity, etc.).

[Not that scale is in anyway equivalent to positive and negative.]

14. Originally Posted by Harold14370
The artist's work in ceramics is legendary.
Although many of those works were later found to have serious structural defects, sadly.

15. I feel sure I have done this before, but I cannot find it....

Suppose I take a segment of the real line and join the two ends together. This we recognize as a circle; grand folk call it the 1-sphere . Now since this is essentially the "same" as our line segment , we might expect to be able to find a one-to-one correspondence between them. This correspondence - an isomorphism on sets, or indeed a homeomorphism on topological spaces - will be given by an invertible function from one to the other.

Of course no such function exists; the map sends the two ends of to same point of - our "join". And since well-behaved functions are not allowed to send a single point in the domain to distinct points in the co-domain, there can be no inverse .

Now there is a theorem (due I think to Dedekind and Pierce) that states that an infinite set is always isomorphic to a proper subset of itself. Since and since isomorphism is an equivalence relation, by transitivity we might expect to be able to do something like the following.

Place our circle anywhere on the real line with our "join" at the North pole, and project each point of "down" to a point in in such a way that none of these projections intersect each other or .

All goes swimmingly until we get to the North pole, where now our projections run parallel to and seem never to meet it.

But we have the perfect construction specifically made for just this purpose, called the "projective real line". This is formed by adjoining what's called the "point at infinity" to to form .

So now our point at the North pole projects to this point at infinity, and a homeomorphism can be recovered, but at some cost; parallel lines meet!

Worse still, since the two projections - "left" and "right" - from the North pole map to the same point in our projective line, this implies that, in , the "end-points" may be considered as the same point. id est .

Don't like the idea? Tough - it is mainstream mathematics!!

16. i know about the Pizza but aparently im on crack so why listen?
ps deulix in answer yes. oh and guitarist 22/7

17. Is having an infinite amount of money the same as having an infinite amount of debt?

18. Originally Posted by ellatha
Is having an infinite amount of money the same as having an infinite amount of debt?
Yes. Thus; current U.S. banking problems. And they didn't even get up to infinite amounts.

19. I may be incorrect here, but instead of the two infinities being the same, would they not be polar opposites? Such as, 10^inf and 10^-inf would be completely opposite vectors? Sorry if I'm completely wrong here, my knowledge of mathematics is infinitesimal.

20. Yes, they would be.

21. i agree with you

22. Originally Posted by Neverfly
Yes, they would be.
Thank you for the clarification.

23. Originally Posted by shlunka
Thank you for the clarification.
Yeah, I had this long drawn out post in mind, but once I put fingers to keyboard... I lost the motivation. Limit theory and Tex editor and a sudden desire to put one in my brainpan....
Originally Posted by fiveworlds
completely right x completes y. i was using sin sin-1 one can never exsist without the other. You mess with it you just create disease like aids and stuff. some things caent be fixed ps sin-1 was shorter tiny amount but still there
What have you been smokin'?

24. Originally Posted by shlunka
I may be incorrect here, but instead of the two infinities being the same, would they not be polar opposites? Such as, 10^inf and 10^-inf would be completely opposite vectors? Sorry if I'm completely wrong here, my knowledge of mathematics is infinitesimal.
No, 10^-inf would be an infinitesimally small number. Negative infintiy would be a large negative number.

25. no i would imagine they are interference patterns carry info but what do i know

26. Originally Posted by fiveworlds
but what do i know
Well, since you post statements like "i was using sin sin-1 one can never exsist without the other. You mess with it you just create disease like aids and stuff." the obvious answer would be "Very little, and you obviously feel compelled to demonstrate that at every opportunity".

27. well yeah but i try my best and the graph is easy same distances 7 or whatever different heights. and everyone knows what viruses are. and p=np also works for movies they run in a set time and you have images of various diff sizes running in polynomial time

28. Originally Posted by fiveworlds
well yeah but i try my best and the graph is easy same distances 7 or whatever different heights. and everyone knows what viruses are. and p=np also works for movies they run in a set time and you have images of various diff sizes running in polynomial time
Is fiveworlds a bot running one of those algorithms for creating grammatically correct sentences using random words?

29. no but i like living outside the box

30. Originally Posted by fiveworlds
no but i like living outside the box
I think the actual wording you were looking for is "out of your tree".

31. Originally Posted by fiveworlds
no but i like living outside the box
Is the land of Gibberish outside the box?

32. Originally Posted by fiveworlds
no but i like living outside the box
By box, do you mean braincase?

33. na just away from strange.by the way what is the box?

34. Originally Posted by fiveworlds
na just away from strange.by the way what is the box?
Strange is usually one of the best contributors to the forum. You'd do well to sidle up next to him and learn all you can. You might even learn what the "box" is. I use the word as you suggested it.

35. oh i know im just playing with ya

36. Originally Posted by fiveworlds
oh i know im just playing with ya
Oh... well.. FINE!

37. learning stuff hmm i do that anyways

38. One graphic indicator that you could consider + and - infinity to be the same (if you haven't read Guitarist's post) is the tangent curve:
tanx.jpg

Unless you believe that a circle isn't actually a circle (i.e. it has discontinuities every 90 degrees) then you might as well take it that each line is directly connected to the next, i.e. disappears at infinity and reappears (after having "gone round") at minus infinity.

39. hey duckie...ozm! I like it! You are coming around. By the way, can anyone "boxed in the pizza box" explain where negative numbers come from?
in order to think outside the box, "the duck" must first step out of the box!

40. HEY WRITE 4U...REFERENCE YOUR January 20th, 2013, 06:49 AM THREAD...A case for an infinitely large cosmos (universe) can be made. But can there be an infinitely small cosmos (universe)?
TRY THE ATOM; IT MIGHT BE SIMILAR TO A SMALL COSMOS.

41. Eaglepass. You are not making sense. The material you are posting is not appropriate for the mathematics section. Please confine your efforts to the pseudoscience or trash can forums.

42. Originally Posted by eaglepass
hey duckie...ozm! I like it! You are coming around. By the way, can anyone "boxed in the pizza box" explain where negative numbers come from?
in order to think outside the box, "the duck" must first step out of the box!
Once again, and as usual, you seem to be confusing your inability to think coherently as "thinking outside the box".

As for "where negative numbers came from", I happen to have a bootleg copy of an old Hollywood draft script for a blockbuster movie (not made) that featured the actual event that "created" negative numbers.
I'll transcribe it later today, sometime in the next couple of hours.

(I figured a Hollywood-type explanation would be more suited to your apparent comprehension, the attendant explosions and gun battles might help you focus and actually learn something).

43. Originally Posted by eaglepass
TRY THE ATOM; IT MIGHT BE SIMILAR TO A SMALL COSMOS.
It might be but it isn't. Not in the slightest.

We all had that idea as children. Some of us later learned to think (there were no boxes involved).

44. In the words of Gandalf - "You shall not eagle-pass"

And on that note, shouldn't we just lock this thread?

45. The Numbers Game - draft script (partial)

Scene, early morning, Egypt 40,0000,0000 AC/ DC, sunrise, open desert

Camera zooms in slowly on a dust trail, which gradually reveals itself to be a string of camels wending their way along a dry track, various riders chat quietly to each other. Suddenly there's a burst of activity and a A-10 Warthog sandworm orbital battlestation disruption happens, one camel falls to the ground with a snap of its leg.

Close up on the screaming camel: They done got me boss! I'm a gonner! Tell my girl I didn't suffer and make sure my kids go to college.

The camel expires slowly, close up remains on his face, fade to:

Later in the day, busy market scene;

Trader 1: Here are the camels my master promised you. But... one died on the way here.
Trader 2: I paid yer boss's skinny ass for 5 camels and he sends me four? What's he trying to pull?
Trader 1: But surely effendi, it's an act of god, you can't blame my master.
Trader 2: Damn right I'm offended, he's tryn'a stiff me!

They start shouting and arguing. Camera pulls back to reveal a group of people, neatly dressed and led by a salt-and-pepper haired man with a rigid military bearing, he reaches into his pocket, retrieves a wallet and shows the contents to the two traders:

Man: Gibbs, NCIS, what's the problem?
Trader 2: His boss is trying to cheat me, sent only four camels when I paid for five. What's it to do with you?
Man (Gibbs): Camels are the ships of the desert, that makes it a naval matter. McGee!
McGee: Boss.
Gibbs: These guys are talking numbers, geek territory, it's your ground. Find out what the problem is.

McGee and the traders go into a lengthy technical discussion, involving the words "four" and "five". McGee nods his head and turns to Gibbs:

McGee: It's like this boss - he sent only four camels when he paid for five.
Gibbs: Good work work McGee. Think you can do anything here?
McGee: Well, I could jiggle the framistat, quantumise the wiggly bit then put my left leg in and shake it all about before...
Gibbs: In English McGee.
McGee: Sorry boss. This guy could owe this guy one camel.
Gibbs: Owe?
McGee: Yeah, He could promise (and cross his heart) that next time he gets a camel it goes straight to this guy.
DiNozzo and David (together): That's crazy, but it just might work.

Gibbs explains this to the two traders, with a look of astonishment they agree and shake hands.

NCIS walk away, another case solved.

Gibbs: Good work McGee, I think your solution will solve a lot of problems in the future. Any idea what we should call this type of numbering?
McGee: Negative boss.
Gibbs, taking the last sip of his coffee: That's good enough for me, write it up.

46. Originally Posted by Dywyddyr
The Numbers Game - draft script (partial)

Scene, early morning, Egypt 40,0000,0000 AC/ DC, sunrise, open desert

Camera zooms in slowly on a dust trail, which gradually reveals itself to be a string of camels wending their way along a dry track, various riders chat quietly to each other. Suddenly there's a burst of activity and a A-10 Warthog sandworm orbital battlestation disruption happens, one camel falls to the ground with a snap of its leg.

Close up on the screaming camel: They done got me boss! I'm a gonner! Tell my girl I didn't suffer and make sure my kids go to college.

The camel expires slowly, close up remains on his face, fade to:

Later in the day, busy market scene;

Trader 1: Here are the camels my master promised you. But... one died on the way here.
Trader 2: I paid yer boss's skinny ass for 5 camels and he sends me four? What's he trying to pull?
Trader 1: But surely effendi, it's an act of god, you can't blame my master.
Trader 2: Damn right I'm offended, he's tryn'a stiff me!

They start shouting and arguing. Camera pulls back to reveal a group of people, neatly dressed and led by a salt-and-pepper haird man with a rigid military bearing, he reaches into his pocket, retrieves a wallet and shows the contents to the two traders:

Man: Gibbs, NCIS, what's the problem?
Trader 2: His boss is trying to cheat me, sent only four camels when I paid for five. What's it to do with you?
Man (Gibbs): Camels are the ships of the desert, that makes it a naval matter. McGee!
McGee: Boss.
Gibbs: These guys are talking numbers, geek territory, it's your ground. Find out what the problem is.

McGee and the traders go into a lengthy technical discussion, involving the words "four" and "five". McGee nods his head and turns to Gibbs:

McGee: It's like this boss - he sent only four camels when he paid for five.
Gibbs: Good work work McGee. Think you can do anything here?
McGee: Well, I could jiggle the framistat, quantumise the wiggly bit then put my left leg in and shake it all about before...
Gibbs: In English McGee.
McGee: Sorry boss. This guy could owe this guy one camel.
Gibbs: Owe?
McGee: Yeah, He could promise (and cross his heart) that next time he gets a camel it goes straight to this guy.
DiNozzo and David (together): That's crazy, but it just might work.

Gibbs explains this to the two traders, with a look of astonishment they agree and shake hands.

NCIS walk away, another case solved.

Gibbs: Good work McGee, I think your solution will solve a lot of problems in the future. Any idea what we should call this type of numbering?
McGee: Negative, boss.
Gibbs, taking the last sip of his coffee: That's good enough for me, write it up.

47. There may well be stupid questions, but they can invoke clever answers...

48. Originally Posted by Duelix

Now, infinity is believed to be 1/0

And negative infinity is -1/0
Excuse me ... .

Thus, is undetermined because ... .

49. There are some interesting formulations of infinite (and infinitesimal) numbers that don't seem to have gotten any coverage on this thread. These are Hyperreal numbers and Surreal numbers.

Both are extensions of Real Numbers, conceptually, in the way Real Numbers are an extension over rational numbers, or rationals over integers.

In any case, within the Hyperreals positive and negative infinite numbers do exist and are not equal.

Originally Posted by Duelix
If we make this a number line:

<------------------------->

then infinity and negative infinity would be at

negative infinity<-----------------------------> infinity

Now, infinity is believed to be 1/0

And negative infinity is -1/0

*****

0 is both negative and positive, so both quantities must be the same, right? This means that infinity and negative infinity are the same.

The simple way of disproving this is to find a function f(x) that approaches some number at infinity, and another number at negative infinity. If any function approaches two different numbers at this point, then my premise would be disproved.

If negative infinity is equal to infinity, then I assume that the number line would be an infinitely narrow ellipse where infinity and negative infinity are the two endpoints. Would this be a new way of approaching limits?

I haven't done calculus yet.

50. Originally Posted by river_rat
Originally Posted by Dywyddyr
The Numbers Game - draft script (partial)

Scene, early morning, Egypt 40,0000,0000 AC/ DC, sunrise, open desert

Camera zooms in slowly on a dust trail, which gradually reveals itself to be a string of camels wending their way along a dry track, various riders chat quietly to each other. Suddenly there's a burst of activity and a A-10 Warthog sandworm orbital battlestation disruption happens, one camel falls to the ground with a snap of its leg.

Close up on the screaming camel: They done got me boss! I'm a gonner! Tell my girl I didn't suffer and make sure my kids go to college.

The camel expires slowly, close up remains on his face, fade to:

Later in the day, busy market scene;

Trader 1: Here are the camels my master promised you. But... one died on the way here.
Trader 2: I paid yer boss's skinny ass for 5 camels and he sends me four? What's he trying to pull?
Trader 1: But surely effendi, it's an act of god, you can't blame my master.
Trader 2: Damn right I'm offended, he's tryn'a stiff me!

They start shouting and arguing. Camera pulls back to reveal a group of people, neatly dressed and led by a salt-and-pepper haird man with a rigid military bearing, he reaches into his pocket, retrieves a wallet and shows the contents to the two traders:

Man: Gibbs, NCIS, what's the problem?
Trader 2: His boss is trying to cheat me, sent only four camels when I paid for five. What's it to do with you?
Man (Gibbs): Camels are the ships of the desert, that makes it a naval matter. McGee!
McGee: Boss.
Gibbs: These guys are talking numbers, geek territory, it's your ground. Find out what the problem is.

McGee and the traders go into a lengthy technical discussion, involving the words "four" and "five". McGee nods his head and turns to Gibbs:

McGee: It's like this boss - he sent only four camels when he paid for five.
Gibbs: Good work work McGee. Think you can do anything here?
McGee: Well, I could jiggle the framistat, quantumise the wiggly bit then put my left leg in and shake it all about before...
Gibbs: In English McGee.
McGee: Sorry boss. This guy could owe this guy one camel.
Gibbs: Owe?
McGee: Yeah, He could promise (and cross his heart) that next time he gets a camel it goes straight to this guy.
DiNozzo and David (together): That's crazy, but it just might work.

Gibbs explains this to the two traders, with a look of astonishment they agree and shake hands.

NCIS walk away, another case solved.

Gibbs: Good work McGee, I think your solution will solve a lot of problems in the future. Any idea what we should call this type of numbering?
McGee: Negative, boss.
Gibbs, taking the last sip of his coffee: That's good enough for me, write it up.

Indeed, they would also have to over come the problem of what zero would represent in number form before any mention of +/- numbers came into it for example: The number zero does not have its own Roman numeral, but the word nulla (the Latin word meaning "none") was used by medieval computists in lieu of 0. So the Romans did not have a Roman numeral for zero but they knew it existed.

51. Originally Posted by andythomasthekey
Indeed, they would also have to over come the problem of what zero would represent in number form before any mention of +/- numbers came into it

Nope.

So the Romans did not have a Roman numeral for zero but they knew it existed.
Romans?

52. You do know what a Roman is don'y you duck? And why would you say no to them having to work out what zero would represent?

53. Originally Posted by andythomasthekey
You do know what a Roman is don'y you duck? And why would you say no to them having to work out what zero would represent?
Yeah I think Julius Caesar had a few of those, they make candles I believe.

54. Fair enough, The Roman Empire better?

55. Originally Posted by andythomasthekey
You do know what a Roman is don'y you duck?
Yup.

And why would you say no to them having to work out what zero would represent?
Let me phrase it this way: WTF do the Romans have to do with it?

56. Well they didn't use zero - why? Not sure myself but they knew it existed, just didn't write about it with a unique numeral.

57. Originally Posted by andythomasthekey
Well they didn't use zero - why?
They didn't like it.

Not sure myself but they knew it existed, just didn't write about it with a unique numeral.
They didn't use it.
But they DID use the abacus - which could let them operate with negative numbers.

58. They didn't like zero but they knew they had to believe in zero, which is nothingness, empty space with stuff in it as daft as it sounded to them. There is no Zero on an abacus either as the balls seem to sit between zero another wall far off to the right. This method has no scale but works fine.

59. Originally Posted by andythomasthekey
There is no Zero on an abacus either
Don't need one for negative numbers.

60. .

61. So they clearly didn't use one, or zero rather? How did they count without zero as in where did they start counting from :/

62. Originally Posted by PhDemon
What makes you think it was the Romans who invented/discovered the number system?

63. Well that's just it, like the Romans the traders and McGee would of had their own way of dealing with Zero by ignoring it it seems.

64. Duelix asked a question and got several perfectly respectable replies. This thread has deteriorated into childishness.