[PDF] definition of injective in real analysis

Definition: Let f : A ? B be a function. ? f is said to be injective or one-to-one or an injection if f(x1) = f(x2) implies x1 = x2 . ? f is said to be surjective or onto or a surjection if f(A) = B . That is, for each y ? B there is some x ? A such that f(x) = y .
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  • What is the meaning of injective?

    Injective means we won't have two or more "A"s pointing to the same "B".
    So many-to-one is NOT OK (which is OK for a general function).
    As it is also a function one-to-many is not OK.
    But we can have a "B" without a matching "A" Injective is also called "One-to-One"

  • What is the logical definition of injective?

    Definition 4.3.1 A function f:A?B is injective if each b?B has at most one preimage in A, that is, there is at most one a?A such that f(a)=b.

  • What is an example of injective in real life?

    The following are a few real-life examples of injective function.
    The name of the student in a class and the roll number of the class.
    The person and the shadow of the person, for a single light source.
    The traveller and his reserved ticket, for traveling by train, from one destination to another.

  • What is an example of injective in real life?

    For example, y=2x, which is both injective (since y1=y2) implies that (x1=x2).
    It is vital to note that no two elements in the domain map to the same codomain value.
    This is referred to as an injective function.
    An injective function is one in which no two domain items map to the same value in the codomain.

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