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Bipolarity

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This is a rather simple question, so it has been rattling my brain recently.

Consider a surjective map ## f : S \rightarrow T ## where both ## S ## and ## T ## are finite sets of equal cardinality. Then is ## f ## necessarily injective? I proved the converse, which turned out to be quite trivial, but this is giving me some trouble indeed. Any initial thoughts on whether it's true (pretty sure it is true!) and how I might go about proving it?

Thanks!

BiP

Consider a surjective map ## f : S \rightarrow T ## where both ## S ## and ## T ## are finite sets of equal cardinality. Then is ## f ## necessarily injective? I proved the converse, which turned out to be quite trivial, but this is giving me some trouble indeed. Any initial thoughts on whether it's true (pretty sure it is true!) and how I might go about proving it?

Thanks!

BiP

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