Hi, can someone please help me with this problem.(adsbygoogle = window.adsbygoogle || []).push({});

Let A be an open subset of the interval [0; 1].

1. Show that the set W = {C(x) : x is in A} is countable or finite.

This is what I have...

Suppose W is an infinite subset of N. Then we have f : W-> N, which

is one-to-one. By the fact that any infinite set contains a countable subset, then W has a countable subset E, since w is infinite. So we have a one-to-one map

g : N ~E -> W. By Cantor-Berstein-Schroeder's Th, W~N.

thanks

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# Homework Help: Show that the set is countable or finite.

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