Function Definition

Discussion in 'Algebra' started by nycmathguy, Jun 28, 2021.

  1. nycmathguy

    nycmathguy

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    Definition of Function

    "A function f from a set A to a set B is a relation that assigns to each element x in the set A exactly one element y in the set B. The set A is the domain (or set of inputs) of the function f, and the set B contains the range (or set of outputs)."

    See Set A and B below.

    A = {(1, 9), (2, 13), (3, 15), (4, 15), (5, 12), (6, 10)}

    I say Set A is a function because every x is assigned to exactly one y.

    Yes?

    B = {(1, 9), (2, 13), (3, 15), (2, 15), (5, 12), (6, 10)}

    I say Set B is not a function because x = 2 is assigned to two different values of y.

    Yes?

    Do not discuss one-to-one functions here. I am not there in the textbook.
     
    nycmathguy, Jun 28, 2021
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  2. nycmathguy

    MathLover1

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    in a function

    "One-to-many" is not allowed, but "many-to-one" is allowed
     

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    MathLover1, Jun 28, 2021
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  3. nycmathguy

    nycmathguy

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    Is my understanding of what a function is incorrect?
     
    nycmathguy, Jun 28, 2021
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  4. nycmathguy

    MathLover1

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    no, your understanding of what a function is correct, I just add it because is easier to remember :)
     
    MathLover1, Jun 29, 2021
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  5. nycmathguy

    nycmathguy

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    Cool. Later on we can discuss one-to-one functions and vertical line test versus horizontal line test but not now. One chapter, one section, one topic, one idea at a time.
     
    nycmathguy, Jun 29, 2021
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