Let $S$ be the set of all even integers, and define a function $f : \mathbf { Z } \longrightarrow \mathbf { S }$ as follows:
$$f ( n ) = 2 n \quad \text { for all integers } n \text {. }$$
(a) Prove that $f$ is one-to-one and onto
(b) Find a formula for the inverse function $f ^ { - 1 }$.
(c) Does the set of all even integers have the same cardinality as the set of all integers? Why or why not?

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The Answer of Let $S$ be the set of all even integers, and define a function $f : \mathbf { Z } \longrightarrow \mathbf { S }$ as follows:
$$f ( n ) = 2 n \quad \text { for all integers } n \text {. }$$
(a) Prove that $f$ is one-to-one and onto
(b) Find a formula for the inverse function $f ^ { - 1 }$.
(c) Does the set of all even integers have the same cardinality as the set of all integers? Why or why not?

Let SSS Be the Set of All Even Integers, and Define a Define

Let $S$ Be the Set of All Even Integers, and Define a Define