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3. Let N denote the nonnegative integers, and Z denote the integers. Define the function g...

3. Let N denote the nonnegative integers, and Z denote the integers. Define the function g : N→Z defined by g(k) = k/2 for even k and g(k) = −(k + 1)/2 for odd k. Prove that g is a bijection.

(a) Prove that g is a function.

(b) Prove that g is an injection

. (c) Prove that g is a surjection.

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