February 4th, 2019, 12:40 PM  #1 
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 125  Counting real numbers
To count the real numbers in [.1,1), remove the decimal point.

February 4th, 2019, 12:53 PM  #2 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,138 Thanks: 872 Math Focus: Wibbly wobbly timeywimey stuff. 
What is [.1,1) after you take away the decimal point? [1, 1) makes no sense! Again with the counting? What exactly are you getting out of this? You know that no one is going to agree with your arguments as they haven't for the last, what, 10 or so threads? Dan 
February 4th, 2019, 12:57 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,472 Thanks: 2039 
I tried it, but most of them went away, saying that counting them would be pointless.

February 4th, 2019, 01:16 PM  #4  
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 125  Quote:
[.1,1) is an interval of real numbers. .1 > 1 .105 > 105 .13 > 13 .333 > 333 Every real number in the INTERVAL [.1,1) maps to a unique natural number. I'm trying to make it as simple as possible.  
February 4th, 2019, 01:24 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,472 Thanks: 2039 
That doesn't help you count them.

February 4th, 2019, 02:43 PM  #6 
Senior Member Joined: Aug 2012 Posts: 2,259 Thanks: 686  
February 4th, 2019, 02:50 PM  #7  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,138 Thanks: 872 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  
February 4th, 2019, 03:44 PM  #8 
Global Moderator Joined: Dec 2006 Posts: 20,472 Thanks: 2039 
That must be what zylo meant, but removing those decimal points doesn't help one count the numbers or prove that they can be counted.

February 4th, 2019, 04:10 PM  #9 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,636 Thanks: 2620 Math Focus: Mainly analysis and algebra  
February 4th, 2019, 04:48 PM  #10 
Member Joined: Jun 2007 From: Richmond, VA Posts: 46 Thanks: 0 
Your example of four numbers above conveniently does not include any reals with an infinite number of (nonzero trailing) digits. There are such reals, but none maps to any integer.


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