Define J : Q Q R by the rule J (r,s) = r + 2s for all (r,s) Q Q. a. Is J one-to-one
Chapter 7, Problem 30(choose chapter or problem)
Define J : \(\mathbf{Q} \times \mathbf{Q} \rightarrow \mathbf{R}\) by the rule \(J(r, s)=r+\sqrt{2} s\) for all \((r, s) \in \mathbf{Q} \times \mathbf{Q}\).
a. Is J one-to-one? Prove or give a counterexample.
b. Is J onto? Prove or give a counterexample.
Text Transcription:
mathbf Q times mathbf Q rightarrow mathbf R
J(r, s)=r+sqrt2 s
(r, s) in mathbf Q times mathbf Q
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