21127 Quiz: Recitation 13 - 10.09
16 Dec 2015
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Examples: consider the set z z. de ne the relation = by setting. (a, b), (c, d) z z. (a, b) = (c, d) ad = bc. Show that = is not an equivalence relation. (hint: think about 0). Amend the de nition so that the relation is de ned on z {0} z {0}. Now, prove that it is an equivalence relation. An in nite binary sequence is just an in nite sequence whose elements are all 0s and 1s. For instance, (0, 1, 0, 1, 0, 1, . is an alternating in nite binary sequence, where all the odd indices corre- spond to 0 and all the even indices correspond to 1. Notationally, we represent an in nite sequence by a letter and an index: a = (an)n n. With the above example a = (0, 1, 0, 1, . we would say a1 = 0 and a2 = 0 and so on.
