So there are many countably innite sets but the set

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Unformatted text preview: nd to STRAIGHT, and for each of those, there are 45 choices of what 18 CHAPTER 1. FOUNDATIONS suit is assigned to the cards with each of the five consecutive integers. Thus, P (STRAIGHT) = = 1.5 10 · 45 52 5 10 · 45 52·51·50·49·48 5·4·3·2 ≈ 0.0039. Countably infinite sets In the previous two sections we discussed how to find the number of elements in some finite sets. What about the number of elements in infinite sets? Do all infinite sets have the same number of elements? In a strong sense, no. The smallest sort of infinite set is called countably infinite, which means that all the elements of the set can be placed in a list. Some examples of countably infinite sets are the set of nonnegative integers Z+ = {0, 1, 2, . . .}, the set of all integers Z = i {0, 1, −1, 2, −2, 3, −3, . . . }, and the set of nonnegative rational numbers.: Q+ = { j : i ≥ 1, j ≥ 1, integers}. Figure 1.4 shows a two dimensional array that contains every positive rational number at least once. The zig-zag...
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