Everything about Injective function
Function that preserves distinctness
In mathematics, an injective function (also known as injection, or one-to-one function) is a function f that maps distinct elements of its domain to distinct elements of its codomain; that is, x1 â x2 implies f(x1) â f(x2) (equivalently by contraposition, f(x1) = f(x2) implies x1 = x2). In other words, every element of the function's codomain is the image of at most one element of its domain. The term one-to-one function must not be confused with one-to-one correspondence that refers to bijective functions, which are functions such that each element in the codomain is an image of exactly one element in the domain. Wikipedia â
đ§ Start here: a 6-step reading path
- Read the overview: Injective functionA 5-minute orientation
- Pick up a classic book: Decision Making HandbookThe most-reprinted book on the subject
- Read the landmark paper: Properly injective spaces and function spacesCited 64 times
- Go sideways: Bijection, injection and surjectionA closely related topic
- Go sideways: Surjective functionA closely related topic
đ Definitions
Noun Synonym of injection (âa relation on sets (X,Y) that associates each element of Y with at most one element of X.â).
đ Landmark papers (most cited)
đ Books worth reading
- đDecision Making HandbookJerry Ramonyai ¡ 2021
Clean CodeRobert C. Martin ¡ 2008- đLeadership, Management and Data ScienceJerry Ramonyai ¡ 2022
The web application hacker's handbookDafydd Stuttard, Marcus Pinto ¡ 2007
Learning PHP, MySQL & JavaScriptRobin Nixon ¡ 2009
Discrete mathematicsNorman Biggs ¡ 1985
NeuroengineeringJoseph D. Bronzino ¡ 2007- đBotulinum Toxins in Clinical Aesthetic Practice 3E, Volume TwoAnthony V. Benedetto ¡ 2017
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đ Related topics
- Bijection, injection and surjection In mathematics, injections, surjections, and bijections are classes of functions distinguished by the manner in which arguments (input expressions fromâŚ
- Surjective function In mathematics, a surjective function (also known as surjection, or onto function /ËÉn.tuË/) is a function f such that, for every element y of the function'sâŚ
- Bijection In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between two sets such that each element of the second set (theâŚ
- Function (mathematics) In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the functionâŚ
- Morphism In mathematics, a morphism is a concept of category theory that generalizes structure-preserving maps such as homomorphism between algebraic structuresâŚ
- List of types of functions In mathematics, functions can be identified according to the properties they have. These properties describe the functions' behaviour under certain conditionsâŚ
- Endomorphism In abstract algebra, an endomorphism is a homomorphism from a mathematical object to itself. More generally in category theory, an endomorphism is a morphismâŚ
- Image (mathematics) In mathematics, the image of a function â f:XâYâ is the set of all â f(x)â such that â xâ belongs to the domain of â fâ . The image by â fâ of an element â xâ âŚ