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Glite Dictionary
bijective

bijective

9.9
A function that pairs each item in one set with exactly one item in another set and vice versa
  • adjective
  • /baɪˈdʒɛktɪv/
  • Specialized
translation icon : bijectiva
  • To prove that a function is bijective, one must show that it is both one-to-one and onto.

So when we're just playing with functions on regular pre calculation classes, we're just only talking about bijective.

Examples

  • A function is bijective if it pairs each element of one set with exactly one element of another set.

  • So it's F is bijective if it's both injective and surjective.

  • So I'll say bijective, that this is an open set.

  • A vector space V is said to be, whoops, isomorphic with a vector W in case there exists A bijective linear mapping T from V to West.

  • In mathematics, a mapping is bijective when it is both injective and surjective.

Synonyms

one-to-one
vsbijective
  • Specialized
5 4.4

Each thing in one group matches exactly one thing in the other group

is the formal mathematical adjective for that exact pairing relation

Surface Forms

bijective positive

Morphology

bijective = bijection (semi-transparent) = bi + ject + ive

Formed from the technical noun 'bijection' with the productive adjectival suffix '-ive'; the morphological process is regular but the base is a specialized mathematical term, so general learners may not infer the meaning from parts alone.

Etymology

Bijective comes from the parts bi- 'two' and -ject 'to throw', with -ject seen in words like project or reject. Think of a 'two-way throw' that makes perfect pairs between two sets: every item on one side is matched with exactly one on the other, which is why a bijective function is one-to-one and onto.