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Microlab May 26th, 2017 12:10 AM

Infinity
 
Infinity is always more than 0 and less than 1!

Joppy May 26th, 2017 12:39 AM

Why

Microlab May 26th, 2017 12:55 AM

Because, anything greater than 1 is combination of 1s. Thanks

Joppy May 26th, 2017 01:46 AM

Are you high?

Benit13 May 26th, 2017 02:22 AM

*Ba-dum tish*

AplanisTophet May 26th, 2017 05:53 AM

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. :p

Microlab May 26th, 2017 09:17 AM

Thank you all. Than here is one question for you guys: how many infinities are in between 0 and 1?

AplanisTophet May 26th, 2017 11:14 AM

Quote:

Originally Posted by Microlab (Post 571188)
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 $2^{\aleph_0}$.

Microlab May 26th, 2017 11:28 AM

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

Maschke May 26th, 2017 12:01 PM

Quote:

Originally Posted by Microlab (Post 571194)
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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