Comments for Higher-dimensional order theory http://math.breckes.org Wed, 09 Sep 2009 05:43:44 +0000 http://wordpress.org/?v=2.9.2 hourly 1 Comment on The two meanings of the word “set” in mathematics by Toby Bartels http://math.breckes.org/2009/03/the-two-meanings-of-the-word-%e2%80%9cset%e2%80%9d-in-mathematics/comment-page-1/#comment-2633 Toby Bartels Wed, 09 Sep 2009 05:43:44 +0000 http://math.breckes.org/?p=9#comment-2633 Maybe you're not here anymore (see the spam above), but I have a comment anyway. When you write >two sets¹ are considered to be “the same” if there exists a bijection between them notice that it's not just a matter of *whether* the two sets¹ are the same (whose answer is a truth value) but fo *how* the two sets¹ are the same (whose answer is a set¹, the set¹ of bijections between them). Other than that, you are (of course) absolutely correct. Maybe you’re not here anymore (see the spam above), but I have a comment anyway.

When you write
>two sets¹ are considered to be “the same” if there exists a bijection between them
notice that it’s not just a matter of *whether* the two sets¹ are the same (whose answer is a truth value) but fo *how* the two sets¹ are the same (whose answer is a set¹, the set¹ of bijections between them).

Other than that, you are (of course) absolutely correct.

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