# Function Definition

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

1. ### 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. ### 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

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Is my understanding of what a function is incorrect?

nycmathguy, Jun 28, 2021
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4. ### 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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