A question about Infinity.

A question came up as I was on another site, the guy known as "Tsadkiel_54904" posted this question.

Could anyone help striaghten him out, or is he lost in thought.

ok, heres my dilema. it is generaly accepted that the number pi is an irrational, infinatly progressive decimal that never repeates. I propesed in class today (we are working on discrete mathematics and, well, one thing led to another) that if pi where truly infinate that it MUST repeate, my idea being that as the sequence progresses the number of possible permutations that yeild a non-repeating decimal decreases. For example:
lets say that you have a ten sided die containing the numbers 0-9 and you roll the die an infinate number of times, what is the probability that the sequence of numbers that you roll will repeate?
The answer (IMO):
100% since the number of sides on the die is finite and the number of chances for repition is infinate then the probability for sucess is 100%

another example:
lets say the universe is infinatly large. assuming that this is true then it must therefore hold an infinate number of planets. lets say that each planet has a small chance of supporting life. what is the probability that a number of planets will support life and how many are there?
The answer:
100% and an infinate number of planets. Why? lets say that you can (somehow) express all the numbers in the sequence
1,2,3,4,5,6,7,8,9...infinity
what if you removed all even numbers from the sequence, how many total numbers will you have?
1,3,5,7,9...infinity
2,4,6,8,10...infinity
therefore infinity divided by 2 = 2 times infinity o.O

back to pi...
the point is that 14159 ect... must repeate given given that it is observed for an infinate perspective. I.e. after a certain point the sequence will repeate simply because there is no other alternative.

if you can please, PLEASE, PROVE ME WRONG. i need to know for sure, its keeping me up at night and i need to get some sleep.

Can anyone help him?



[Edited on 29-4-2004 by HumptyDumpty]

For starters, infinity divided by 2 does = 2 times infinity.

Because of the property of infinity, it can not be changed unless you have other infities involved.

Second, he is right about pi repeating. But he is kinda off in the way he is thinking.

It repeats after infinity.

The repeating IS infinity.

He talks about inifinity as if it is a finite thing. It is not. Yes, it has repeating portions, but they repeate infinitly, as do OTHER portions.

Basicly, he makes a pointless circular argument.

1,3,5,7,9...infinity
2,4,6,8,10...infinity
therefore infinity divided by 2 = 2 times infinity

I have time to address this one, the pi question would take more time and explanation then I have to give tonight.

What is infinity? Infinity means unlimited, limitless, without end. How can you multiply unlimited by 2? Or divide it? infinity * 2 = infinity. infinity / 2 = infinity. infinity + 2 = infinity. Infinity - 1 (who knows the reference?! ) = infinity.

You can go one a neverending journey. If someone else also goes on a never ending journey, and you combined the time they spent on this journey, it would still be never ending. It wouldn't be never ending * 2

OK thanks guys, that seem to work for me. Ill direct him to have a look at this. Thanks.

Ironicly, we contradicted eachother

The Primary Problem with what this person is doing is that they are trying to use 'Infinity' as if it's some kind of 'Number' with a Real Value in formulas involving other True Real Numbers. 'Infinity' can't really be used like that, since it's not the same as numbers like 1 or 2 or 3 etc. It's a concept. For example:
Saying Infinity/2 or Infinity+1 or whatever might as well be 'Cheese/2' or 'Toe Fungus+1' or something.

Another thing about Infinity is it's a concept that can become extremely more complicated than any normal number, even if you could try and use it in a formula with other real numbers. One strange property of 'Infinity' is that, in terms of conceptual thinking, Infinity=Everything & Nothing=Nothing, and yet True Nothingness is Infinite also, in that it's Infinite Nothingness. In a way this can lead to different types of Logic Paradoxes where Infinity=Zero. It just depends on where you want to start on your Number scale.

Then there is also something called 'Sets' and 'Infinite Sets'. This is where you have more than One Infinite Value at the same time. But how can that be? How can you have more than One Infinity? Well, for example:
There are an Infinite Amount of Negative Numbers.
There are an Infinite Amount of Positive Numbers.
Since Neg. and Pos. Numbers are not the same, you have Two Differnet 'Infinite Sets' at the same time, which do not fit in the other set.
Once again though, You also have the 'Infinite Set of All Numbers' where both Pos. and Neg. Numbers belong. So now you have One 'Infinte Set' which is made of Two Independent 'Infinite Sets'!! And this can go on and on until your hair turns grey, you forget why you even started thinking of the idea and you're about one step away from therapy!!

Certain groups of numbers in the Pi series do repeat. Random chance dictates that. There is even a Pi calculator which gave the largest repeating section and allowed you to call up any of the series. (I don't remember the link though)

To really be a repeating number it would have to repeat a series over and over, in its entirety. This is something Pi will not do before reaching infinity.

Originally posted by Kano
Certain groups of numbers in the Pi series do repeat. Random chance dictates that. There is even a Pi calculator which gave the largest repeating section and allowed you to call up any of the series. (I don't remember the link though)

To really be a repeating number it would have to repeat a series over and over, in its entirety. This is something Pi will not do before reaching infinity.

Not sure if this is the Pi pattern search tool you're talking about or not, but it's a fun one anyway!!

Pi Searcher lets you search for any string of digits (up to 120 of them) in the first 100 million digits of Pi. You can also show any substring of Pi.
www.angio.net...

I get what he means about pi, if it does truly go on for infinity then is MUST repeat itself, because there is an infinite amount of chances that it will. BUT as the infinity of pi goes on the chance that it will repeat exactly becomes not really smaller because it goes on for infinity but the string of numbers that have to repeat will become larger and larger. ie the chance that 15324 will repeat in the decimals of a number that goes on for infinity is 100% but the chance of having an infinite number that repeats itself out of an inifnity of numbers is quite impossible, so therefore pi must start repeating itself.

(i no u could say that the first infinity is x and its out of 2x, and i guess that could work too, but then the chance is 0.infinity 0's 1 percent)

yes... think about it...

Ah yes mOjOm, that looks like it. Cheers

quik: yes certain groups of numbers will repeat. But the whole series will not repeat over and over.

Originally posted by quiksilver
...but the chance of having an infinite number that repeats itself out of an inifnity of numbers is quite impossible, so therefore pi must start repeating itself.
...

Actually, from what you are saying one would jump to the conclusion that pi must'n repeat itself. Like you said, the chances that an infinit sequnce of numbers to repeat is virtualy none!!