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Alternative ways to say “if and only if”?

So when I come across mathematical definitions like "A function is continuous if...."A space is compact if....","Two continuous functions are homotopic if.....", etc when is it okay to assume that the definition includes the converse as well?

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    Yes, definitions are "if and only if" statements. The "only if" part holds trivial content though, because it is *defined* like that.2012-07-10
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    In fact, definitions *should* be interpreted that way. Personally, following the lead of my favorite undergraduate professor, I always use the "if and only if" format, and when I use it in class, I make the (verbal) point of saying that it is an "if and only if" because it is a definition.2012-07-10

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