Give a example of a function from N to N (naturals) that is a) one-to-one and onto b) onto but not one-to-one
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What about $\displaystyle f(n) = \left\lfloor {\frac{n}{2}} \right\rfloor $? Which part does that answer?
Originally Posted by pila0688 Give a example of a function from N to N (naturals) that is a) one-to-one and ontoo An obvious answer: f(n)= n. b) onto but not one-to-one Try mapping each even number, 2n, into n and each odd number, 2n+ 1 into n. That is, 1->1, 2->1, 3->2, 4->2, etc.
Would f(n) = n^2 be onto but not 1-1?
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