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May 26th, 2017, 12:10 AM   #1
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Infinity

Infinity is always more than 0 and less than 1!
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May 26th, 2017, 12:39 AM   #2
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Why
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May 26th, 2017, 12:55 AM   #3
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Because, anything greater than 1 is combination of 1s. Thanks
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May 26th, 2017, 01:46 AM   #4
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Are you high?
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May 26th, 2017, 02:22 AM   #5
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*Ba-dum tish*
Thanks from Joppy
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May 26th, 2017, 05:53 AM   #6
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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.
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May 26th, 2017, 09:17 AM   #7
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Thank you all. Than here is one question for you guys: how many infinities are in between 0 and 1?
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May 26th, 2017, 11:14 AM   #8
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Quote:
Originally Posted by Microlab View Post
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 $2^{\aleph_0}$.
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May 26th, 2017, 11:28 AM   #9
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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
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May 26th, 2017, 12:01 PM   #10
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Quote:
Originally Posted by Microlab View Post
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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