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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 zigzag...
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 Spring '08
 Zahrn
 The Land

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