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- https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/Discrete_Structures/06%3A_Functions/6.03%3A_Injections_Surjections_and_BijectionsFunctions are frequently used in mathematics to define and describe certain relationships between sets and other mathematical objects. In addition, functions can be used to impose certain mathematical...Functions are frequently used in mathematics to define and describe certain relationships between sets and other mathematical objects. In addition, functions can be used to impose certain mathematical structures on sets. In this section, we will study special types of functions that are used to describe these relationships that are called injections and surjections.
- https://math.libretexts.org/Courses/Monroe_Community_College/MTH_220_Discrete_Math/5%3A_Functions/5.4%3A_Onto_Functions_and_Images%2F%2FPreimages_of_SetsGiven a function f:A→B, and C⊆A, the image of C under f is defined as f(C)={f(x)∣x∈C}. In words, f(C) is the set of all the images of the elements...Given a function f:A→B, and C⊆A, the image of C under f is defined as f(C)={f(x)∣x∈C}. In words, f(C) is the set of all the images of the elements of C. Given a function f:A→B, and D⊆B, the preimage D of under f is defined as f−1(D)={x∈A∣f(x)∈D}. Hence, f−1(D) is the set of elements in the domain whose images are in C.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/A_Spiral_Workbook_for_Discrete_Mathematics_(Kwong)/06%3A_Functions/6.04%3A_Onto_FunctionsOne-to-one functions focus on the elements in the domain. We do not want any two of them sharing a common image. Onto functions focus on the codomain. We want to know if it contains elements not assoc...One-to-one functions focus on the elements in the domain. We do not want any two of them sharing a common image. Onto functions focus on the codomain. We want to know if it contains elements not associated with any element in the domain.
- https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Book%3A_Mathematical_Reasoning__Writing_and_Proof_(Sundstrom)/06%3A_Functions/6.03%3A_Injections_Surjections_and_BijectionsFunctions are frequently used in mathematics to define and describe certain relationships between sets and other mathematical objects. In addition, functions can be used to impose certain mathematical...Functions are frequently used in mathematics to define and describe certain relationships between sets and other mathematical objects. In addition, functions can be used to impose certain mathematical structures on sets. In this section, we will study special types of functions that are used to describe these relationships that are called injections and surjections.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/03%3A_Functions/3.01%3A_FunctionsThis page explains essential concepts of mathematical mapping, particularly focusing on functions, including definitions of key terms like function, surjective, injective, bijection, and inverse mappi...This page explains essential concepts of mathematical mapping, particularly focusing on functions, including definitions of key terms like function, surjective, injective, bijection, and inverse mapping. It emphasizes that a function maps each input to one output, and onto functions connect all codomain elements. The existence of inverse mappings depends on the one-to-one property of functions.
