a. Define f : Z Z by the rule f (n) = 2n, for all integers n. (i) Is f one-to-one Prove
Chapter 7, Problem 10(choose chapter or problem)
a. Define f : \(Z \rightarrow Z\) by the rule f (n) = 2n, for all integers n.
(i) Is f one-to-one? Prove or give a counterexample.
(ii) Is f onto? Prove or give a counterexample.
b. Let 2Z denote the set of all even integers. That is, \(2 \mathbf{Z}=\{n \in \mathbf{Z} \mid n=2 k, \text { for some integer } k\}\). Define h: \(\mathbf{Z} \rightarrow 2 \mathbf{Z}\) by the rule h(n) = 2n, for all integers n. Is h onto? Prove or give a counterexample.
Text Transcription:
Z rightarrow Z
2 mathbf Z ={n in mathbf Z mid n=2k, for some integer k}
mathbf Z rightarrow 2 mathbf Z
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