surjective

/(ˌ)sər-ˈjek-tiv/ (ame, mw)

surjective — adjective

  • surjectivepositive
  • more surjectivecomparative
  • most surjectivesuperlative

1. relating to a mathematical rule or mapping where every value in the set of possi

1.形容詞C1
釋義

relating to a mathematical rule or mapping where every value in the set of possible outputs is actually reached by at least one input value — the function's range covers its entire target set without gaps.

例句

Professor Jason proved that f(x)=2x from integers to even integers is surjective.

prove + that-clause + is surjective for logical deduction

On the final exam, Lucía had to identify which of five functions were surjective.

同義詞
  • onto

    more common in introductory courses and less formal math writing; identical meaning

文法句型

function + be + surjective

surjective + function

用法筆記

Commonly taught alongside injective (one-to-one) and bijective (both properties). In introductory textbooks the synonym 'onto' is more frequent. Predicative use ('the function is surjective') and attributive use ('a surjective function') are equally natural.

常見錯誤

❌A surjective function sends each input to a different output.
✅A surjective function reaches every possible output value.
💡the wrong sentence describes an injective (one-to-one) function, not a surjective one.