Dictionary

antidifference en · NOUN

Etymology

Etymology tree Proto-Indo-European *h₂ent- Proto-Indo-European *-s Proto-Indo-European *h₂énts Proto-Indo-European *-i Proto-Indo-European *h₂énti Ancient Greek ᾰ̓ντῐ́ (ăntĭ́) Ancient Greek ἀντι- (anti-)der. English anti- Proto-Indo-European *dwóh₁ ▲ Proto-Indo-European *trísinflu. Proto-Indo-European *d(w)is- Proto-Italic *dis- Latin dis- Proto-Indo-European *bʰer- Proto-Indo-European *-eti Proto-Indo-European *bʰéreti Proto-Italic *ferō Latin ferō Latin differō Latin differēns Proto-Indo-European *-(i)yós Proto-Italic *-ijos Proto-Italic *-ios Old Latin -ios Latin -ius Latin -ia Latin differentiader. Old French differencebor. Middle English difference English difference English antidifference From anti- + difference.

Meanings

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

Forms

Relateds

antiderivative

Synonyms

indefinite sum