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(Solved): 7. Let \( k \) be a strictly positive integer. Let \( A \) be a set with \( |A| \geq k+1 \), and \( ...




7. Let \( k \) be a strictly positive integer. Let \( A \) be a set with \( |A| \geq k+1 \), and \( B \) a set with \( |B|=k
7. Let \( k \) be a strictly positive integer. Let \( A \) be a set with \( |A| \geq k+1 \), and \( B \) a set with \( |B|=k \). Let \( f: A \rightarrow B \) be a function. Show that \( f \) cannot be injective. 8. Construct a sequence of 16 strictly positive integers that has no increasing or decreasing subsequence of five terms.


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The set A with |A|?k+1, B be a set with |B|=k, and the map f:A?B function is given. The main objective is to prove the function can not be injective.
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