# Mathematical Tools for Data Mining: Set Theory, Partial

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Imagine that each person is represented by a point in the plane (which we think of as a vertex of a graph—see Chap. 8). Introduction to stochastic processes and their applications in science and industry. What is curious CHAPTER 6 Counting Arguments 119 here is that we do not care about what x is. Connect two points by a solid line if those two people are acquainted. The ﬁrst few amount of time: there are an inﬁnite number of strings in ¦0, 1¦ 138.2.3 Exercise Prove that the lexical ordering on ¦0, 1¦ The canonical ordering on ¦0, 1¦ 139.1.1 Example 1110 comes before 00001 because it is shorter, and 0011 comes before 0101 because 0011 is 3 in binary and 0101 is 5. 139.1.2 Example In the canonical ordering of ¦0, 1¦ 139.1.3 Fact The canonical ordering is linear and, unlike the lexical ordering, there are only a ﬁnite number of strings between any two strings. in the lexical ordering and in the canonical ordering. (Answer on page 251.) 139.1.6 Exercise Prove that the canonical ordering on ¦0, 1¦ and that there are only a ﬁnite number of strings between any two given strings.

Pages: 616

Publisher: Springer; 2008 edition (August 15, 2008)

ISBN: 1848002009

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