## equivalence between a set and the subset of its subset

Is it true that: If A is not equivalent to its subset A1. Then A is not equivalent to any subset of A1?
 PhysOrg.com science news on PhysOrg.com >> Leading 3-D printer firms to merge in $403M deal (Update)>> LA to give every student an iPad;$30M order>> CIA faulted for choosing Amazon over IBM on cloud contract
 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.
 actually this is trivial. I just learnt all this the complicated way, .i.e. proving cantor bernstein without the well ordering theorem.

 Similar discussions for: equivalence between a set and the subset of its subset Thread Forum Replies Calculus & Beyond Homework 2 Set Theory, Logic, Probability, Statistics 22 Calculus & Beyond Homework 5 Calculus & Beyond Homework 2 Set Theory, Logic, Probability, Statistics 10