This is thus a theorem that they are equivalent for algebraic structures see Homomorphism § Monomorphism for more details.Ī function f is injective or one-to-one.
Learn about function notation by watching this tutorial. A function basically relates an input to an output, theres an input, a relationship and an output. However, in the more general context of category theory, the definition of a monomorphism differs from that of an injective homomorphism. What is Function Notation Note: Every see 'f (x)' in your math That's function notation It's a way to indicate that an equation is a function. For all common algebraic structures, and, in particular for vector spaces, an injective homomorphism is also called a monomorphism. Types of Functions in Maths An example of a simple function is f (x) x 2. Set notation uses sets to say explicitly where the function is or isnt. It takes an element of R2, like (2,1), and gives a value that is a real number (i.e., an element of R), like f(2,1)3. the domain) and their outputs (known as the codomain) where each input has exactly one output, and the output can be traced back to its input. The domain of a function is the set of values that we are allowed to plug into. It is sometimes denoted by or, where f is the function. 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.Ī homomorphism between algebraic structures is a function that is compatible with the operations of the structures. A function in maths is a special relationship among the inputs (i.e. In mathematics, the domain of a function is the set of inputs accepted by the function.
(Equivalently, x 1 ≠ x 2 implies f( x 1) ≠ f( x 2) in the equivalent contrapositive statement.) In other words, every element of the function's codomain is the image of at most one element of its domain. 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 that is, f( x 1) = f( x 2) implies x 1 = x 2.
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