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May 6, 2010 at 11:43 comment added gowers I'd think of that not as a belief that people are likely to have so much as a statement that looks moderately plausible and doesn't have an obvious counterexample. In other words, it's not something that people unthinkingly assume, because they don't tend to think about it at all. But perhaps I'm wrong about that and it is routinely used as a lemma by inexperienced algebraists.
May 6, 2010 at 0:53 comment added Qiaochu Yuan See also mathoverflow.net/questions/1058/when-does-cantor-bernstein-hold .
May 6, 2010 at 0:10 history answered Kerry CC BY-SA 2.5