Question: Please answer exercise 7. Write legibly and in complete sentences. Thank you! Exercise 7 . Let A be an infinite set and let B be

Please answer exercise 7. Write legibly and in complete sentences. Thank you!

Exercise 7 . Let A be an infinite set and let B be a set such that A is equinumerous to a subset of B. Show that B is infinite . 13. 24 Remark . It is possible for an infinite set to be equinumerous to a proper subset of itself . For instance , the set w = $0. 1 , 2 . ... . is equinumerous to the proper subset N = [ 1, 2, 3, ... ], because if we let f ( no ) = ~ + 1 for all ~ Ew, then I is a bijection from w to N. As the next result shows , this phenomenon does not occur for finite sets . ( By the way , it is this that proves that w really is infinite . )

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