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 May 26th, 2017, 12:10 AM #1 Member   Joined: May 2017 From: USA Posts: 31 Thanks: 0 Infinity Infinity is always more than 0 and less than 1!
 May 26th, 2017, 12:39 AM #2 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,225 Thanks: 420 Math Focus: Yet to find out. Why
 May 26th, 2017, 12:55 AM #3 Member   Joined: May 2017 From: USA Posts: 31 Thanks: 0 Because, anything greater than 1 is combination of 1s. Thanks
 May 26th, 2017, 01:46 AM #4 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,225 Thanks: 420 Math Focus: Yet to find out. Are you high?
 May 26th, 2017, 02:22 AM #5 Senior Member   Joined: Apr 2014 From: Glasgow Posts: 2,019 Thanks: 665 Math Focus: Physics, mathematical modelling, numerical and computational solutions *Ba-dum tish* Thanks from Joppy
 May 26th, 2017, 05:53 AM #6 Senior Member   Joined: Jun 2014 From: USA Posts: 299 Thanks: 21 I'm a sucker for threads that ponder the infinite, even when they lead to nonsense. I saw this, got interested, clicked on it, and then wow... just wow. You got me. Good one.
 May 26th, 2017, 09:17 AM #7 Member   Joined: May 2017 From: USA Posts: 31 Thanks: 0 Thank you all. Than here is one question for you guys: how many infinities are in between 0 and 1?
May 26th, 2017, 11:14 AM   #8
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 Originally Posted by Microlab Thank you all. Than here is one question for you guys: how many infinities are in between 0 and 1?
That depends on what you mean by "infinities."

If I consider the number of different infinite subsets of rational numbers that can be created from the rationals on the interval (0, 1), then the answer is a cardinal number commonly denoted $2^{\aleph_0}$.

 May 26th, 2017, 11:28 AM #9 Member   Joined: May 2017 From: USA Posts: 31 Thanks: 0 Thanks again! Well, how should I describe for example: 0.11111... or 0.99999... or 0.12451234512345... Do they belong to "infinity" ? Just curious. Thanks
May 26th, 2017, 12:01 PM   #10
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 Originally Posted by Microlab Thanks again! Well, how should I describe for example: 0.11111... or 0.99999... or 0.12451234512345... Do they belong to "infinity" ? Just curious. Thanks
They're finite real numbers. They happen to have infinitely long nonrepeating decimal expansions. That's because the decimal representation in general is flawed.

To clarify this, consider the decimal .1234512345...

Now that looks like it encodes an infinite amount of information. But actually it has a repeating block so it's a rational number. In fact it's $\frac{12345}{99999}$. So it only encodes two whole numbers, not infinitely many.

A number is an abstract object that may have many different representations. A real number has a decimal representation (sometimes two) but the representation is not the number.

It does happen to be the case that decimal representation is flawed. Some numbers have two different representations. Others only encode a finite amount of information, yet their decimal representation is infnite, as we saw with $.1234512345 \dots$

So we shouldn't confuse a finite number with its infinite decimal representation. In fact all real numbers are finite numbers.

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