bijective

1 9.9

A function that pairs each item in one set with exactly one item in another set and vice versa

adjective
/baɪˈdʒɛktɪv/

Specialized

: 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

20 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.