Let $A,B$ be two sets.
Is there necessarily an injection from $A$ to $B$ or an injection from $B$ to $A$ ?
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Try using finite $A$'s and $B$'s. – kingW3 Nov 09 '15 at 22:51
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@kingW3 How is that helpful? – Nov 09 '15 at 22:53
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See also: Is the class of cardinals totally ordered? – Nov 09 '15 at 22:54
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@NormalHuman I guess it was a bit of a broad statement,anyway I had my intentions how to lead him to answer. – kingW3 Nov 09 '15 at 23:02
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Doesn't "|A|< |B|" or "A has smaller cardinality than B" MEAN there exist an injective function from A to B that is not a surjection? If not, what definition of "<" are you using. – user247327 Nov 09 '15 at 23:21