Prove that if functions $f : A \rightarrow B$ and $h : B \rightarrow C$ are total, then $h \circ f$ is total.
How do I prove that $h \circ f$ is total?
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$\begingroup$
functions
elementary-set-theory
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0@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. – 2012-05-04
1 Answers
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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.
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0Ah thanks! That makes sense. h is total, so, because the entire codomain of f is within B, $h(f(a))$ must be defined. – 2012-05-04