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I'm reading Godement's Analysis 1. He proceeds to give "naive demonstrations of certain facts about elementary set theory" and there is this one:

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I'm a bit confused: He says "Choose $a\in Y-X$" but as $Y \subset X$ wouldn't $Y-X=\emptyset$? Also, in the end he says $x_0\not\in Y$ but the just declared $x_0=a\in Y$. What am I missing here?

Red Banana
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  • It seems to me the existence of such a bijection f is unnecessarily complicated as well. https://math.stackexchange.com/questions/2450729/prove-that-every-infinite-set-has-a-countable-subset gives an alternate proof – emilg Apr 24 '25 at 03:12
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    @emilg the proof seems to be using a different definition of infinite than the one we have here :) – Malady Apr 24 '25 at 03:22

1 Answers1

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It is a typo. Choose $a\in X-Y$.

Anne Bauval
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