# Thread: Infinity between 0 and 1

1. Hello everybody. (0,1) . A number range. But when you take a number in this range, it can go forever. like 1/2, 1/24248319321479234791414857126412... . It will get closer to 0 but never will be 0?

2.

3. Yes, there are infinitely many numbers inbetween 0 and 1.

I think there's a video about it on YouTube. I'll go search for it and edit this reply.

Interesting stuff to think about!

4. Try to answer this!!!
If a you take a ruler (knowing there are an infinite amount of places in between) and I slide my finger all the way across how is it possible?
If my finger has an infinite amount of places to stop at, how would I ever move it across the ruler?!

5. Originally Posted by MindlessMath
Try to answer this!!!
If a you take a ruler (knowing there are an infinite amount of places in between) and I slide my finger all the way across how is it possible?
If my finger has an infinite amount of places to stop at, how would I ever move it across the ruler?!
I would venture to guess it is because you did not stop your finger at the infinite number of places. From a math perspective, fractions can also have infinite places when turned into decimal. 1/3 or PI for example.

6. Originally Posted by MindlessMath
Try to answer this!!!
If a you take a ruler (knowing there are an infinite amount of places in between) and I slide my finger all the way across how is it possible?
If my finger has an infinite amount of places to stop at, how would I ever move it across the ruler?!

You have broken mathematics. Stop doing that.

7. Originally Posted by Cogito Ergo Sum
You have broken mathematics. Stop doing that.
That made my day!!!

8. Originally Posted by Mayflow
Originally Posted by MindlessMath
Try to answer this!!!If a you take a ruler (knowing there are an infinite amount of places in between) and I slide my finger all the way across how is it possible?If my finger has an infinite amount of places to stop at, how would I ever move it across the ruler?!
I would venture to guess it is because you did not stop your finger at the infinite number of places. From a math perspective, fractions can also have infinite places when turned into decimal. 1/3 or PI for example.
I have never really put any thought into that question, so your guess is as good as mine! It is a good brain teaser though.

9. Originally Posted by DevPhysics
Hello everybody. (0,1) . A number range. But when you take a number in this range, it can go forever. like 1/2, 1/24248319321479234791414857126412... . It will get closer to 0 but never will be 0?
Actually that number will not ever get any closer to 0 than 1/2424831932147923479141485712641299999999...
If you want to approach 0 you need something more like 1/999...

10. That's not right. 1/X will approach 0 as long as X increases. 1.X won't, but that's something else entirely.

11. So.... we are all content that the "smallest" number not zero in the real (open) interval (0,1) is rational?

Umm...

12. There are infinite numbers between 1 and 0. Also, there are infinite natural numbers and the fractions between them. So... that means that there are infinities bigger than others?

NO. They are infinity.

13. Originally Posted by YellowKazooie8
There are infinite numbers between 1 and 0. Also, there are infinite natural numbers and the fractions between them. So... that means that there are infinities bigger than others?
Yes. And the proof is remarkably simple.

14. Originally Posted by Guitarist
So.... we are all content that the "smallest" number not zero in the real (open) interval (0,1) is rational?
I'm pretty sure it isn't. But I'm not sure how to prove it...

15. Originally Posted by Strange
Originally Posted by YellowKazooie8
There are infinite numbers between 1 and 0. Also, there are infinite natural numbers and the fractions between them. So... that means that there are infinities bigger than others?
Yes. And the proof is remarkably simple.
Infinity is infinity. You can't do math with such numbers (like, infinity x 2, or infinity x infinity). There is no such thing as bigger infinities because if there was, it wouldn't be infinity. It is a rather simple logic

16. Originally Posted by YellowKazooie8
It is a rather simple logic
As I say, there is a very simple proof you are wrong. But we know from your past that you are not interested in reality if it contradicts your beliefs.

17. Originally Posted by YellowKazooie8
Infinity is infinity.
But not all infinities are the same.

You can't do math with such numbers (like, infinity x 2, or infinity x infinity).
Oh dear...
Someone (no names mentioned) has apparently never heard of transfinite mathematics.

There is no such thing as bigger infinities because if there was, it wouldn't be infinity.
Wrong.

It is a rather simple logic
While you're pretty good at simple, you're not very good at logic.

18. Originally Posted by Strange
Originally Posted by YellowKazooie8
There are infinite numbers between 1 and 0. Also, there are infinite natural numbers and the fractions between them. So... that means that there are infinities bigger than others?
Yes. And the proof is remarkably simple.

Where can I find it?

19. Originally Posted by Cogito Ergo Sum
Where can I find it?
Cantor's diagonal argument - Wikipedia, the free encyclopedia

20. Originally Posted by Strange
Originally Posted by Cogito Ergo Sum
Where can I find it?
Cantor's diagonal argument - Wikipedia, the free encyclopedia
That is pretty Strange to me

21. Try mapping the reals between 0 and 1 to all natural (whole) numbers.
It can be shown that there are more numbers between 0 and 1 than there are whole numbers, yet the number of whole numbers is infinite.
How One Infinity Can Be Bigger Than Another

22. Originally Posted by YellowKazooie8
Originally Posted by Strange
Originally Posted by Cogito Ergo Sum
Where can I find it?
Cantor's diagonal argument - Wikipedia, the free encyclopedia
That is pretty Strange to me
But as it uses real logic (rather than "this is what I believe so I will call it logic") it is an unassailable proof.

23. Originally Posted by Strange
Originally Posted by Cogito Ergo Sum
Where can I find it?
Cantor's diagonal argument - Wikipedia, the free encyclopedia
Originally Posted by Dywyddyr
Try mapping the reals between 0 and 1 to all natural (whole) numbers.
It can be shown that there are more numbers between 0 and 1 than there are whole numbers, yet the number of whole numbers is infinite.
How One Infinity Can Be Bigger Than Another

Thank you for the links!
It clarified a lot (although the theoretical proof presented on Wikipedia is quite abstract, but that is due to my limited mathematical knowledge).

24. Here's a YouTube video (from an actual mathematician) about the topic: https://www.youtube.com/watch?v=elvOZm0d4H0. I think it explains things fairly well.

25. So this Is why the hound never catches the fox. That's what I thought, too. I don't know Math. just math.
Question: After 27 halving's of matter, we arrive at the atom, no ? And the Quantum begins. Is this correct ?
Sagan is the source.

26. Half a meter 27 times and you reach something around the thickness of a cell membrane: https://www.wolframalpha.com/input/?i=2^-27+meters

If you double a hydrogen atom's width 27 times, you get something about the size of an ant: https://www.wolframalpha.com/input/?...ydrogen+widths, http://en.wikipedia.org/wiki/Orders_...itude_(length)

27. Okay, the troll is gone. Can we have a rational discussion about The Reals now...

Originally Posted by MindlessMath
Try to answer this!!!
If a you take a ruler (knowing there are an infinite amount of places in between) and I slide my finger all the way across how is it possible?
If my finger has an infinite amount of places to stop at, how would I ever move it across the ruler?!
Originally Posted by Euclid
αʹ. Σημεῖόν ἐστιν, οὗ μέρος οὐθέν.
Originally Posted by Guitarist
So.... we are all content that the "smallest" number not zero in the real (open) interval (0,1) is rational?

Umm...
No such element as the "smallest number not zero" may exist in the Reals, else they be denumerable.
Did I get that partially right at least?

28. Originally Posted by MindlessMath
Originally Posted by Mayflow
Originally Posted by MindlessMath
Try to answer this!!!If a you take a ruler (knowing there are an infinite amount of places in between) and I slide my finger all the way across how is it possible?If my finger has an infinite amount of places to stop at, how would I ever move it across the ruler?!
I would venture to guess it is because you did not stop your finger at the infinite number of places. From a math perspective, fractions can also have infinite places when turned into decimal. 1/3 or PI for example.
I have never really put any thought into that question, so your guess is as good as mine! It is a good brain teaser though.
I would like to attempt an explanation for this problem, since it caused me to join this forum when I was about to go on with my regular web surfing.

I imagined two arguments, that I hope you kind people will examine:

(1) I´ll just say that it is basicly true, in the very same terms of the question. It takes an infinite amount of time to do so, since a second can be divided samewise, endlessly. And we can go on with that in mind: our finger is infinite. You will soon demolish known space into paradoxes. It might sound like a critic, but it isn´t. Maybe such perspective leads us to why some physicist think time is an ilusion, and, avoiding human consciousness of movement, things are still, and changes take place at some timeless level.

(2) Following that line of thought, we can also think of this: as time is dividable ad infinitum, those space subdivisions are neutralized by time subdivisions. So, if a milimeter is rationally fragmented a trillion times, time is divided too, and we walk through an infinitely small fraction of space in infinitely small fraction of time, thereby giving our conciousness the relief of grasping only those segments of time and space that match our livelihood.

I personally can´t say which one I believe in. You tell me, fellas.

(Yes, you got it, I learned my english from books so not only I have a wrong notion of english grammar but I use puffed vocabulary.)

29. Originally Posted by Leopardi
since a second can be divided samewise, endlessly
Uh, Planck time?

And we can go on with that in mind: our finger is infinite.
Infinitely divisible isn't quite the same as infinite.

and changes take place at some timeless level.
How does anything happen without time?

(Yes, you got it, I learned my english from books so not only I have a wrong notion of english grammar but I use puffed vocabulary.)
We've had (maybe still got) native English speakers considerably worse than you're showing here.

30. And we can go on with that in mind: our finger is infinite.
Infinitely divisible isn't quite the same as infinite.

and changes take place at some timeless level.
How does anything happen without time?

(Yes, you got it, I learned my english from books so not only I have a wrong notion of english grammar but I use puffed vocabulary.)
We've had (maybe still got) native English speakers considerably worse than you're showing here.[/QUOTE]

Hi, pal.

We can agree on this: if you slice a cake infinitely, the result would be an infinite number of cake slices. Likewise with time and space. That´s the sense of the teaser. That of the ruler and the finger, if I must...

Regarding nonexistence of time, I´ve been wondering the same. But physicists can´t solve any of my questions. Julian Barbour has no time to answer my letters. He thinks he´s too funny, don´t you say?

Cheers.

31. Ah, Julian Barbour. I bought his book just after it came out, but haven't got round to reading it yet 1.
Not enough time. *cough*.

But: There is no general agreement that the ideas expressed in the book have any predictive power and thereby constitute a scientific theory.

1 I buy books when I see them. On the basis that when I WANT them I'll either not find them for sale or won't have the money.

32. Originally Posted by Dywyddyr
Ah, Julian Barbour. I bought his book just after it came out, but haven't got round to reading it yet 1.
Not enough time. *cough*.

But: There is no general agreement that the ideas expressed in the book have any predictive power and thereby constitute a scientific theory.
.
You said it well, sir.

You´ll see I´m not leveraging my explanation on Barbour´s theory. All I´m saying is that when you reach some limits on language construction of mathematical issues, like the one that you stumble upon in the said problem, you realize time is not so easy to apprehend, and its non existence is only another possibility within the wide range of reality interpretations, that might be outside the common sense of thing.

I believe the answer to that tricky question of the ruler can be found on my second argument, that could be translated to be your own. "Infinitely divisible isn´t infinite". When you ask yourself: does my hand go through infinite places inbetween the ruler, the answer could be: "Yes, if you abstractly divide the space infinitely. But infinite pieces of something don´t add up to be an infinite amount as a whole, so your hand goes through the little pieces of space in equaly small time periods, that when are added start to seem as what they truly are: finite, just as the ruler."

Pretty obvious, perhaps, but obvious is frequently the ladder to get out from problematic questions.

What do you think of this, mate?

33. I'm never far away you pompous...members of the scientific reality counsel. Pretty soon I'll own the fucking bridge. You've been blinded by science, become all swelled-up. Comes the deluge, brothers. Now would be a good time to find god. She blinded me with science. Good song. Bad science.

34. Originally Posted by umbradiago
I'm never far away you pompous...members of the scientific reality counsel. Pretty soon I'll own the fucking bridge. You've been blinded by science, become all swelled-up. Comes the deluge, brothers. Now would be a good time to find god. She blinded me with science. Good song. Bad science.
Okay, I'll bite. What are you going on about?

35. This. If you guys ever met a brilliant troll, you'd walk right past. The topic was infinite mathematics or something. I asked a physics question, and some got snobbish. Stayed snobbish, actually. All your education doesn't hide the fact you won't admit when your wrong. -Jaws
Originally Posted by GiantEvil
Okay, the troll is gone. Can we have a rational discussion about The Reals now...

Originally Posted by MindlessMath
Try to answer this!!!
If a you take a ruler (knowing there are an infinite amount of places in between) and I slide my finger all the way across how is it possible?
If my finger has an infinite amount of places to stop at, how would I ever move it across the ruler?!
Originally Posted by Euclid
αʹ. Σημεῖόν ἐστιν, οὗ μέρος οὐθέν.
Originally Posted by Guitarist
So.... we are all content that the "smallest" number not zero in the real (open) interval (0,1) is rational?

Umm...
No such element as the "smallest number not zero" may exist in the Reals, else they be denumerable.
Did I get that partially right at least?

36. Scientific inquiry doesn't require good manners. In discourse, it's useful.

37. Originally Posted by umbradiago
Scientific inquiry doesn't require good manners. In discourse, it's useful.
If you are upset by the "troll" comment, for what it's worth I thought it was a reference to YellowKazooie8, who in my opinion deserved it.

38. Thanks. That would make me an idiot. Seems fair, in this case. No, I don't want a blindfold.

39. Originally Posted by me.
Okay, the troll is gone. Can we have a rational discussion about The Reals now...
^No that wasn't directed at you, and it's most salient purpose was the pun at the end.

40. OK chaps. settle down and do some mathematics.......

I will say that the cardinality of some set associates to that set a cardinal number. Note that there are infinitely many natural numbers, but by the definition of the natural numbers, they can, at least in principle, be counted.

One associates the cardinal number to the natural numbers to denote this fact.

Now Cantor's diagonal argument (referenced earlier) shows that the Real numbers are uncountable and obviously of infinite cardinality which is denoted by the cardinal number

I assert, without argument, that if 2 (or more) sets can be placed, element by element, in a one-to-one correspondence, then they have the same cardinality.

I now assert, with proof, that the open interval can be placed in one-to-one correspondence with , the Real numbers i.e. that his interval is uncountably infinite.

I consider . The correspondence is self-evident. Likewise the inverse . Thus the correspondence and

The correspondence with inverse is one-to-one between and

Therefore the correspondence is one-to-one from to .

Thus both and each have cardinality

41. Didn't Georg Cantor realize that various kinds of infinities exist?

42. Originally Posted by jrmonroe
Didn't Georg Cantor realize that various kinds of infinities exist?
See post #18

43. assume you move across every possible point in an infinitesmall amount of time

44. Soo this means between two edges, there can be an infinity? I also thought about that. You can implement this also in real life. Let's say there are two points called A and B. I am moving from A to B but for example if I take a step first then I take the half of it and it keeps going like that. My steps keeps getting smaller and can get smaller forever. But I am moving. I am getting closer to B but I will never reach B?

45. Originally Posted by Mayflow
Originally Posted by MindlessMath
Try to answer this!!!
If a you take a ruler (knowing there are an infinite amount of places in between) and I slide my finger all the way across how is it possible?
If my finger has an infinite amount of places to stop at, how would I ever move it across the ruler?!
I would venture to guess it is because you did not stop your finger at the infinite number of places. From a math perspective, fractions can also have infinite places when turned into decimal. 1/3 or PI for example.
I didn't t read all the comments so i figure someone answered it..but i'll amuse myself and take a stab at it. The problem with this problem is that you think of your finger as something that is finite, when in reality it has an infinite amount of space like any other space. So, you're sliding and infinite amount of space over an infinite amount of space..Since not all infinities are of equal value, I guess it makes sense to slide an infinite amount of space over an infinite amount of space?

46. Originally Posted by phillies5351
The problem with this problem is that you think of your finger as something that is finite, when in reality it has an infinite amount of space like any other space.
Whut?
I'm pretty damned sure none of my fingers have an infinite amount of space.

47. Originally Posted by Dywyddyr
Originally Posted by phillies5351
The problem with this problem is that you think of your finger as something that is finite, when in reality it has an infinite amount of space like any other space.
Whut?
I'm pretty damned sure none of my fingers have an infinite amount of space.

Since one's fingers point to one's own mind, I think you are right here.

48. Originally Posted by Mayflow
Since one's fingers point to one's own mind
Pure bollocks.

49. Originally Posted by Dywyddyr
Pure bollocks.
Well, at least you do soliloquy quite well.

50. Originally Posted by Mayflow
Originally Posted by Dywyddyr
Pure bollocks.
Well, at least you do soliloquy quite well.
And you do drivel even better.
Do you agree with phillies5351 that fingers are "infinite in volume"?
If so, why?
On what basis?

51. Originally Posted by EugeneT
Yes, there are infinitely many numbers inbetween 0 and 1.

I think there's a video about it on YouTube. I'll go search for it and edit this reply.

Interesting stuff to think about!

Thank you for the share!

52. Originally Posted by Dywyddyr
Originally Posted by Mayflow
Originally Posted by Dywyddyr
Pure bollocks.
Well, at least you do soliloquy quite well.
And you do drivel even better.
Do you agree with phillies5351 that fingers are "infinite in volume"?
If so, why?
On what basis?

I was wrong in saying infinite amount of space. What I meant to say is that the length of your finger is similar to an inch in the sense that there is an infinite amount of values between 0 and the 1 inch mark. You're not moving something that doesn't have an infinite amount of values between something that does.

53. Originally Posted by YellowKazooie8
Originally Posted by Strange
Originally Posted by YellowKazooie8
There are infinite numbers between 1 and 0. Also, there are infinite natural numbers and the fractions between them. So... that means that there are infinities bigger than others?
Yes. And the proof is remarkably simple.
Infinity is infinity. You can't do math with such numbers (like, infinity x 2, or infinity x infinity). There is no such thing as bigger infinities because if there was, it wouldn't be infinity. It is a rather simple logic
Intuitively, sure, infinity is infinity. Intuitively, all things should be wholly deterministic. Intuitively, .999 repeating is slightly different than 1. Sometimes, though, the things that seem like they are the most reasonable as far as common sense is concerned are wrong. Human intuition is fallible. .999 repeating is 1, infinities have varying sizes, and the universe doesn't follow deterministic rules all of the time. Saying that it doesn't make sense changes none of these facts.

54. Originally Posted by phillies5351
Originally Posted by Dywyddyr
Originally Posted by Mayflow
Originally Posted by Dywyddyr
Pure bollocks.
Well, at least you do soliloquy quite well.
And you do drivel even better.
Do you agree with phillies5351 that fingers are "infinite in volume"?
If so, why?
On what basis?

I was wrong in saying infinite amount of space. What I meant to say is that the length of your finger is similar to an inch in the sense that there is an infinite amount of values between 0 and the 1 inch mark. You're not moving something that doesn't have an infinite amount of values between something that does.
I figured the part I bolded is what you meant. Staying true to the ideas in Original Post here. Your last sentence that I didn't bolden, I did not understand, though. BTW, It is my Birthday today. I wonder if I have infinite Birthdays?

55. I'm saying that a point on the ruler ( or table) has an infinite amount of stopping points on your finger..it's not like your finger is an arbitrary point moving over a never ending axis..maybe that doesn't help with the brain teaser. I guess a moving finger can go through an infinite amount of stopping points because its at each point for for infinitesimal amount of time..that sounds more right in my mind. Moving your finger across that ruler almost seems like a non-mathamtical proof that not all infinities are the same.

56. Originally Posted by phillies5351
I'm saying that a point on the ruler ( or table) has an infinite amount of stopping points on your finger..it's not like your finger is an arbitrary point moving over a never ending axis..maybe that doesn't help with the brain teaser. I guess a moving finger can go through an infinite amount of stopping points because its at each point for for infinitesimal amount of time..that sounds more right in my mind. Moving your finger across that ruler almost seems like a non-mathamtical proof that not all infinities are the same.
I have two different viewpoints on this - there should be a third I think.. I'll come up with it shortly...

1. Physically if you kept moving your finger a over a period of time, the distance would be covered and not infinite.

2. If you could move in half distances the motion of the finger would get infintisimally small and it would be an infinite distance and you would never reach the end. - Let me change that - the distance would not be infinite, it would be just that your movements become infinite, and can never reach the destination.

3. OK here will be my third idea... This is something I think I partially thought on because of a certain passage in Plato's story of Phaedrus... I think there are two different types of realities or existence. One is of the physical and while it may exist in size and complexities beyond even counting, it may also be just illusionary creations of mind - so while it may seem to exist for millenia after millenia it is in a sense infinite - because the possibilities are infinite - but it is infinite (and eternal) only by the powers of the mind.

Everthing in what the Buddhists call Samsara is transitory and always in flux and always changing. - They typicaly call this unsatisfactory - but that is where I hugely differ, as I think it is perfection personified and all mind created. Mind itself I consider as unborn and undying - similar I think to what some think that God is or some think that Nirvana is.

57. Isn't this just another version of Zeno's Paradox?

58. Originally Posted by Mayflow
Originally Posted by phillies5351
I'm saying that a point on the ruler ( or table) has an infinite amount of stopping points on your finger..it's not like your finger is an arbitrary point moving over a never ending axis..maybe that doesn't help with the brain teaser. I guess a moving finger can go through an infinite amount of stopping points because its at each point for for infinitesimal amount of time..that sounds more right in my mind. Moving your finger across that ruler almost seems like a non-mathamtical proof that not all infinities are the same.
I have two different viewpoints on this - there should be a third I think.. I'll come up with it shortly...

1. Physically if you kept moving your finger a over a period of time, the distance would be covered and not infinite.

2. If you could move in half distances the motion of the finger would get infintisimally small and it would be an infinite distance and you would never reach the end. - Let me change that - the distance would not be infinite, it would be just that your movements become infinite, and can never reach the destination.

3. OK here will be my third idea... This is something I think I partially thought on because of a certain passage in Plato's story of Phaedrus... I think there are two different types of realities or existence. One is of the physical and while it may exist in size and complexities beyond even counting, it may also be just illusionary creations of mind - so while it may seem to exist for millenia after millenia it is in a sense infinite - because the possibilities are infinite - but it is infinite (and eternal) only by the powers of the mind.

Everthing in what the Buddhists call Samsara is transitory and always in flux and always changing. - They typicaly call this unsatisfactory - but that is where I hugely differ, as I think it is perfection personified and all mind created. Mind itself I consider as unborn and undying - similar I think to what some think that God is or some think that Nirvana is.

two other thoughts:

1- if you keep dividing space on the ruler and not the finger, your finger ( or a point on your finger ) would be infinitely bigger than the divided space.

2- space isn't linear ( I've heard of debates about this)

59. Or maybe we're just not thinking in the right dimensions ( saw that as an explanation for Zeno's paradox)

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