• Thumbnail for Bijection
    Bijection (redirect from Bijective function)
    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 (the...
    19 KB (2,508 words) - 09:01, 28 May 2025
  • 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...
    17 KB (2,589 words) - 07:48, 3 July 2025
  • } The function f is bijective (or is a bijection or a one-to-one correspondence) if it is both injective and surjective. That is, f is bijective if, for...
    76 KB (11,410 words) - 20:15, 22 May 2025
  • Thumbnail for Inverse function
    f exists if and only if f is bijective, and if it exists, is denoted by f − 1 . {\displaystyle f^{-1}.} For a function f : X → Y {\displaystyle f\colon...
    43 KB (5,224 words) - 09:30, 6 June 2025
  • Thumbnail for Bijection, injection and surjection
    Bijection, injection and surjection (category Functions and mappings)
    one element of the domain; that is, if the function is both injective and surjective. A bijective function is also called a bijection. That is, combining...
    15 KB (2,207 words) - 15:52, 23 October 2024
  • unique; the function f may map one or more elements of X to the same element of Y. The term surjective and the related terms injective and bijective were introduced...
    17 KB (1,948 words) - 14:12, 3 July 2025
  • if there exist injective functions f : A → B and g : B → A between the sets A and B, then there exists a bijective function h : A → B. In terms of the...
    20 KB (2,374 words) - 11:57, 23 March 2025
  • Thumbnail for Isomorphism
    set Y with a binary relation S then an isomorphism from X to Y is a bijective function f : X → Y {\displaystyle f:X\to Y} such that: S ⁡ ( f ( u ) , f (...
    19 KB (2,733 words) - 16:31, 5 June 2025
  • ways correspond to way w. Bijective proofs prove that two sets have the same number of elements by finding a bijective function (one-to-one correspondence)...
    5 KB (727 words) - 16:43, 10 February 2024
  • generated by these functions. The set of all bijective functions f: X → X (called permutations) forms a group with respect to function composition. This...
    37 KB (3,772 words) - 08:50, 25 February 2025
  • the sets in two combinatorial classes have equal size, by finding a bijective function that maps one set one-to-one onto the other. This technique can be...
    4 KB (400 words) - 06:03, 27 December 2024
  • Thumbnail for Probability density function
    variable with joint density f. If y = G(x), where G is a bijective, differentiable function, then y has density pY: p Y ( y ) = f ( G − 1 ( y ) ) | det...
    30 KB (4,947 words) - 17:28, 9 July 2025
  • (mouse) tumors The Gompertz function is a one-to-one correspondence (also known as an Bijective function) and so its inverse function can be explicitly expressed...
    21 KB (3,154 words) - 08:30, 13 August 2024
  • partial functions. A partial function is said to be injective, surjective, or bijective when the function given by the restriction of the partial function to...
    15 KB (2,055 words) - 16:59, 20 May 2025
  • the inverse function f − 1 {\displaystyle f^{-1}} need not be continuous. A bijective continuous function with a continuous inverse function is called a...
    63 KB (9,324 words) - 15:49, 8 July 2025
  • maps I {\displaystyle I} bijectively onto the open interval J = f ( I ) {\displaystyle J=f(I)} , and such that the inverse function f − 1 : J → I {\displaystyle...
    42 KB (7,930 words) - 16:02, 27 May 2025
  • Thumbnail for Inverse function rule
    calculus, the inverse function rule is a formula that expresses the derivative of the inverse of a bijective and differentiable function f in terms of the...
    9 KB (1,789 words) - 13:15, 27 April 2025
  • Thumbnail for Trigonometric functions
    define a true inverse function, one must restrict the domain to an interval where the function is monotonic, and is thus bijective from this interval to...
    77 KB (10,653 words) - 18:24, 2 July 2025
  • Thumbnail for Cardinal number
    among the infinite cardinals. Cardinality is defined in terms of bijective functions. Two sets have the same cardinality if, and only if, there is a one-to-one...
    26 KB (3,834 words) - 18:49, 17 June 2025
  • cardinality in terms of bijective functions: two sets have the same cardinality if, and only if, there exists a bijective function between them. Between...
    16 KB (2,381 words) - 03:46, 28 April 2025
  • Thumbnail for Complex number
    the interval (−π, π]. This leads to the complex logarithm being a bijective function taking values in the strip R + + i ( − π , π ] {\displaystyle \mathbb...
    91 KB (12,021 words) - 17:33, 29 May 2025
  • Thumbnail for Identity function
    identity function on X is clearly an injective function as well as a surjective function (its codomain is also its range), so it is bijective. The identity...
    6 KB (629 words) - 16:15, 2 July 2025
  • The Möbius function μ ( n ) {\displaystyle \mu (n)} is a multiplicative function in number theory introduced by the German mathematician August Ferdinand...
    22 KB (3,124 words) - 07:23, 26 June 2025
  • as Hilbert spaces). In other words, a unitary transformation is a bijective function U : H 1 → H 2 {\displaystyle U:H_{1}\to H_{2}} between two inner product...
    2 KB (278 words) - 13:42, 4 December 2023
  • Thumbnail for Gross tonnage
    historical convenience. Since gross tonnage is a bijective function of ship volume, it has an inverse function, namely ship volume from gross tonnage, but...
    8 KB (869 words) - 02:14, 3 March 2025
  • Thumbnail for Stereographic projection
    perpendicular to the diameter through the point. It is a smooth, bijective function from the entire sphere except the center of projection to the entire...
    49 KB (6,215 words) - 14:29, 24 June 2025
  • Thumbnail for Homeomorphism
    or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are...
    13 KB (1,643 words) - 16:09, 12 June 2025
  • a surjection or onto function. Bijective function: is both an injection and a surjection, and thus invertible. Identity function: maps any given element...
    13 KB (1,407 words) - 00:18, 19 May 2025
  • Thumbnail for Weierstrass elliptic function
    \mathbb {R} /2\pi \mathbb {Z} } is chosen to be the domain, so the function is bijective. In a similar way one can get a parameterization of C g 2 , g 3...
    28 KB (5,213 words) - 00:19, 7 July 2025
  • with pV as its argument. Of course any bijective function will do, but for convenience's sake a linear function is the best. Therefore, we define it as...
    17 KB (2,512 words) - 10:29, 20 June 2025