May 26th, 2017, 01:10 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, 01:39 AM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,401 Thanks: 479 Math Focus: Yet to find out. 
Why

May 26th, 2017, 01:55 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, 02:46 AM  #4 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,401 Thanks: 479 Math Focus: Yet to find out. 
Are you high?

May 26th, 2017, 03:22 AM  #5 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,073 Thanks: 695 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
*Badum tish*

May 26th, 2017, 06:53 AM  #6 
Senior Member Joined: Jun 2014 From: USA Posts: 310 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, 10:17 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, 12:14 PM  #8  
Senior Member Joined: Jun 2014 From: USA Posts: 310 Thanks: 21  Quote:
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, 12:28 PM  #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, 01:01 PM  #10  
Senior Member Joined: Aug 2012 Posts: 1,620 Thanks: 411  Quote:
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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