Injective

C2 16+

Pronunciation: /ɪnˈdʒɛktɪv/

Definitions of injective

adjective relating to or characterized by injection, especially denoting a function in which each element of the domain is mapped to a distinct element in the codomain

Example Sentences

A1 An injective function is a mathematical function where each element of the domain maps to a unique element in the codomain.

A2 In mathematics, an injective function is also known as a one-to-one function because each element in the domain corresponds to exactly one element in the codomain.

B1 The concept of injective functions is important in algebra and calculus, as it helps determine if a function has a unique inverse.

B2 When studying functions in advanced mathematics, it is crucial to understand the properties of injective functions and how they relate to surjective and bijective functions.

C1 A function is injective if and only if it preserves distinctness: for every pair of distinct elements in the domain, their images under the function are also distinct.

C2 The injective property of a function can be proven using mathematical techniques such as proof by contradiction or direct proof methods.

Examples of injective in a Sentence

formal The function is injective if each element in the domain maps to a unique element in the codomain.

informal An injective function means that each input has its own distinct output.

slang If the function is injective, it means each number gets its own special spot.

figurative Being injective is like having a one-to-one correspondence between two sets.

Grammatical Forms of injective

past tense

injected

plural

injectives

comparative

more injective

superlative

most injective

present tense

injects

future tense

will inject

perfect tense

has injected

continuous tense

is injecting

singular

injective

positive degree

injective

infinitive

to inject

gerund

injecting

participle

injecting

Origin and Evolution of injective

First Known Use: 1938 year
Language of Origin: Latin
Story behind the word: The word 'injective' originated from the Latin word 'injectus' meaning 'thrown in'.
Evolution of the word: Originally used in mathematics to describe a function that preserves distinctness, the term 'injective' has since been adopted in various fields such as computer science and biology to refer to a similar concept of one-to-one correspondence.