equivalence between a set and the subset of its subset

by batballbat
Tags: equivalence, subset
batballbat is offline
Nov21-12, 11:52 AM
P: 127
Is it true that: If A is not equivalent to its subset A1. Then A is not equivalent to any subset of A1?
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Norwegian is offline
Nov22-12, 07:03 AM
P: 144
You should consider also informing us about the relevant equivalence relation, as the truth or falsity of your statement heavily depends on that information.

For example, if you for your eq.rel. use existence of a bijection, the statement is true, but other relations, like having same parity, will render your statement false.
batballbat is offline
Nov22-12, 07:41 AM
P: 127
actually this is trivial. I just learnt all this the complicated way, .i.e. proving cantor bernstein without the well ordering theorem.

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