TITLE: Alternative ways to say "if and only if"?
QUESTION [20 upvotes]: There are some scenarios about which I would like to get some confirmation:

when defining a concept A, 

We call A, if ... [definition of
  concept A]

Does "if" here mean equivalence
instead of just sufficiency? Is it
incorrect to replace "if" with "if
and only if"?

For precisely what condition is
   B satisfied?

Does "precisely" mean asking for
necessary and sufficient condition
for B?
Some other ways to say "if and only
if" / "necessary and sufficient"?

Some references that summarize some standard terminologies in Mathematics  such as this one?
Thanks and regards!

REPLY [3 votes]: When we write (for example) "we say that an integer is odd if it is not divisible by $2$", the statement does not explicitly deny that we might describe as odd a number that is divisible by $2$. The reason for ruling out the latter circumstance is that it would make the definition pointless. Thus, in definitions, there is an implicit message "either this definition is pointless or you may assume that it applies only if the stated conditions hold". As long as the author has the respect of the reader, the latter can be counted on to fill in the "and only if" part of the definition. If it became seen as necessary to put "and only if" in definitions, it would need to go in every definition henceforth, and any author failing to comply would have to worry about seeming wrong.
This has more to do with the conventions of discourse than with formal logic.