MHB Identity Function: Definition, Examples & Properties

Thread starter dana1
Start date May 11, 2014
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Function Identity

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The identity function is defined as a function that maps every element of a set to itself, denoted as $id_A: A \to A$. It is characterized as a bijection, meaning it is both injective and surjective. The composition of the identity function with any other function $f$ results in the original function, expressed as $f \circ id_A = f$. The discussion highlights that the identity function maintains the properties of bijections when composed with other functions. Understanding the identity function is crucial for grasping more complex function properties in mathematics.

May 11, 2014

dana1

hey,
question is attached

thanks in advance!

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May 11, 2014

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dana said:

hey,
question is attached

thanks in advance!

Hi dana!

Well... since $id_A: A\to A$ is a bijection, it seems fair to me that $f \circ g: A \to A$ given by $f \circ g: a \mapsto a$ is also a bijection...

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