# Using if and not “if and only if” in definitions [duplicate]

We often see the word "if" in connection with definitions e.g

y is a solution of $x^{'}=f(x,t)$ if $y^{'}=f(y,t)$ or

A metric space is complete if every cauchy sequence converges.

Why isnt it written if and only if in general in this context?

## marked as duplicate by Cameron Buie, Community♦Jul 15 '18 at 15:46

• "A if B" means $B \Rightarrow A$. "A iff B" means $B \iff A$. – mvw Jul 15 '18 at 16:06