Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Prove that if functions $f : A \rightarrow B$ and $h : B \rightarrow C$ are total, then $h \circ f$ is total.

share|improve this question
1  
"Total" does not normally mean "surjective". It means everywhere defined, i.e. an actual function rather than a partial function. –  Chris Eagle May 4 '12 at 19:13
    
@Chris: I see. Well, it might not be a duplicate per se then. However if you look at the answer (or the argument) you can easily see it is really just the same thing. –  Asaf Karagila May 4 '12 at 19:22

1 Answer 1

up vote 2 down vote accepted

Take any $a\in A$. Since $f$ is total, then $f(a)$ is defined, and an element of $B$, and since $h$ is total, then $h(f(a))$ is defined.

share|improve this answer
    
Ah thanks! That makes sense. h is total, so, because the entire codomain of f is within B, $h(f(a))$ must be defined. –  Minden Petrofsky May 4 '12 at 19:16

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.