Prove the following infinite version of the pigeon-hole principle: Suppose that X is an infinite subset, and Y is a finite subset. Then for any function f : X →Y, there is a y E Y such that |ƒ−¹(y)] > ∞. (Hint: By contradiction: Assume that [ƒ−¹(y)| < ∞ for all y ≤ Y and use the fact that Y is finite to obtain a contradiction using the generalized pigeonhole principle)

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List all of the possible ways to choose 2 different flowers from the list: daisy, orchid, petunia, tulip. Be systematic. Give some kind of justification. Justifications include verbal explanations of how you approached the problem or a list. An example of one way to choose 2 flowers from the list is daisy and orchid. Order does not matter so daisy/orchid and orchid/daisy are the same pair. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). BIUS Paragraph Arial XQ HQ ¶ "" Ω Θ P = = = X I!!! 10pt 用网 X₂ ள எ † A {;} +] < ABC T₂ 57 Ⓒ Ky O WORDS POWERED BY TINY