# I want clear a point about definitions. [duplicate]

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.

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