different between antiderivative vs antidifference

English

anti- +? derivative

antiderivative (plural antiderivatives)

(calculus) A function whose derivative is a given function; an indefinite integral
Synonyms: primitive, integral

anti- +? difference

antidifference (plural antidifferences)

A function F(x) is the antidifference of f(x) if F(x+1)-F(x)=f(x).
If f(x)=b^x then F(x)=b^x/(b-1)+C is the general antidifference since F(x+1)-F(x) = [b^x+1/(b-1)+C] - [b^x/(b-1)+C] = (b^x+1-b^x)/(b-1) = b^x = f(x).

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