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I want know wether "defnitions" are if and only if. For example if a set satsfies all four group axioms we say it is group but then we go other way also.

thank you.

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    $\begingroup$ Yes they are. Always. $\endgroup$ – Adam Hughes Mar 25 '16 at 18:09
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    $\begingroup$ Yes, $A$ "defined as" $B$ is equivalent to $A \Leftrightarrow B$. $\endgroup$ – M47145 Mar 25 '16 at 18:10

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