08-24-2009-lecture

08-24-2009-lecture - ... (What is this number?) ....

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Calculus 1551, Section 4. August 24, 2009 Notes The integers: Z = { ... - 2 , - 1 , 0 , 1 , 2 ,... } . The rational numbers: Q = { a/b | a,b Z ,b 6 = 0 } . The real numbers: R = “all the numbers on the number line.” But how do you locate a number on the number line? Putting integers on a line 1) Pick a line . 2) Pick a segment U as a unit of measure. 3) Pick a point O on and a direction on . 4) Using U mark the integers on , placing 0 and O and increasing in the chosen direction. Locating the rational numbers on the line If we want to find the location of a particular rational number, say 15 / 7, we divide U into 7 equal pieces, and we find the point we reach by putting 15 copies end-to end. How about decimal notation? You certainly are aware that in decimal notation, some numbers have infinite names. For example: π = 3 . 1415926 ... 1 3 = 0 . 333 ... 2 . 142857142857142857 ... (What is this number? You’ve seen it before!) 0 . 999
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Unformatted text preview: ... (What is this number?) . 101001000100001000001 ... (Is this number rational or irrational?) When we write a non-teminating decimal, we get some information about the location of the number from each truncation. When we say between, below, we mean the inclusive between. = 3 . ??? ... is between 3 and 4 = 3 . 1??? ... is between 3 + 1 10 and 3 + 2 10 = 3 . 14??? ... is between 3 + 1 10 + 4 100 and 3 + + 1 10 + 5 100 1 What number is: between 0 and 1 between 3 10 and 4 10 between 3 10 + 3 100 and 3 10 + 4 100 between 3 10 + 3 100 + 3 1000 and 3 10 + 3 100 + 4 1000 etc. What number is: between 0 and 1 between 9 10 and 1 between 9 10 + 9 100 and 1 between 9 10 + 9 100 + 9 1000 and 1 etc. 2...
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This note was uploaded on 11/23/2011 for the course MATH 1551 taught by Professor Malisoff during the Fall '08 term at LSU.

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08-24-2009-lecture - ... (What is this number?) ....

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