Counting real numbers To count the real numbers in [.1,1), remove the decimal point. 
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 
I tried it, but most of them went away, saying that counting them would be pointless. 
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[.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. 
That doesn't help you count them. 
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Dan 
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. 
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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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