Prove that |R[0,1)| <= |F| where F is the set of all functions from N to {0,1}

Asked Feb 05 '14 at 23:43

Active Feb 05 '14 at 23:43

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I believe that I need to show that there's a one-to-one function from R[0,1) to F and that I can do this by associating the decimal expansion .b_1b_2b_3... etc with a function f(n) that is either 0 or 1 based on some property of the digit b_n in the decimal expansion. I'm having trouble coming up with such a function.

asked Feb 05 '14 at 23:43

user126571

2

And what is $R[0,1)$? The interval $[0, 1) \subseteq \mathbb{R}$? – Feb 05 '14 at 23:48
1

Why decimal? Binary might be easier. – Carsten S Feb 05 '14 at 23:48
Yes to T. Bongers. – user126571 Feb 05 '14 at 23:51

Prove that |R[0,1)| <= |F| where F is the set of all functions from N to {0,1}

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