Equivalence: They agree everywhere where both are defined and one is undefined where ever the other one is.
What's the difference between equality and equivalence of recursive functions?
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logic
computer-science
computability
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0I would say they are the same notion - have you encountered them being used differently? – 2017-02-28
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0See [Recursive function : Definition : Strong equality](https://en.wikipedia.org/wiki/%CE%9C-recursive_function#Definition) – 2017-02-28
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0But why do theyou define Equality? Isn't it just the usual Notion? – 2017-02-28
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0The "natural" def of *equality* between *functions* would be : $f(n)=g(n)$ for every $n$. But what happens when the two have not the same dom of definition ? Recursive functins are not *total* (i.e. not everywhere defined) and thus the above def must be adapted. – 2017-03-02