Continued fractions Yann BUGEAUD Let x0,x1,... be real numbers
... a continued fraction, provided that the limit exists. The aim of this Section is to show how a real number ξ can be expressed as ξ = [x0 ; x1 , x2 , . . .], where x0 is an integer and xn a positive integer for any n ≥ 1. We first deal with the case of a rational number ξ, then we describe an algorit ...
... a continued fraction, provided that the limit exists. The aim of this Section is to show how a real number ξ can be expressed as ξ = [x0 ; x1 , x2 , . . .], where x0 is an integer and xn a positive integer for any n ≥ 1. We first deal with the case of a rational number ξ, then we describe an algorit ...
ppt
... Rational numbers – the set of all numbers that can be expressed as a quotient of integers, with denominator 0 • Irrational numbers – the set of all numbers that can NOT be expressed as a quotient of integers • Real numbers – the set of all rational and irrational numbers combined ...
... Rational numbers – the set of all numbers that can be expressed as a quotient of integers, with denominator 0 • Irrational numbers – the set of all numbers that can NOT be expressed as a quotient of integers • Real numbers – the set of all rational and irrational numbers combined ...
The Value of the Number Line
... vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. ...
... vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. ...
Components of the Real Number System
... Maybe these developed with the creation of money….?? To remember, we’ve gone “inte” debt to get negative numbers! Still just points; no line yet. ...
... Maybe these developed with the creation of money….?? To remember, we’ve gone “inte” debt to get negative numbers! Still just points; no line yet. ...
solutions - One Mathematical Cat
... 19. −1 is an integer, but not a whole number 20. positive integers: 1 , 2 , 3 , . . . 21. nonnegative integers: 0 , 1 , 2 , 3 , . . . ...
... 19. −1 is an integer, but not a whole number 20. positive integers: 1 , 2 , 3 , . . . 21. nonnegative integers: 0 , 1 , 2 , 3 , . . . ...
Lecture 12
... • Take the case of ten people in a row: there are 10 choices for the first person; then, since we’ve chosen the first person, there are 9 choices for the second; then 8 choices for the third; and so forth. So overall, there are 10! (= 10 * 9 * 8 * …. 1) ways of ...
... • Take the case of ten people in a row: there are 10 choices for the first person; then, since we’ve chosen the first person, there are 9 choices for the second; then 8 choices for the third; and so forth. So overall, there are 10! (= 10 * 9 * 8 * …. 1) ways of ...
A B
... assumption has led to a contradiction. This forces us to accept the only possible alternative to the original assumption. That is, it is not possible to set up a one-to-one correspondence between and , which means that is uncountable. ...
... assumption has led to a contradiction. This forces us to accept the only possible alternative to the original assumption. That is, it is not possible to set up a one-to-one correspondence between and , which means that is uncountable. ...
Math131A Set 2 June 30, 2013
... 9.1. For each sequence, use the theorems in Section 9 to prove it converges to some real number, or prove that it diverges. [Note that the first three are the same as those in 8.2 above.] 2n−5 (a) 6n−5 (b) (c) (d) ...
... 9.1. For each sequence, use the theorems in Section 9 to prove it converges to some real number, or prove that it diverges. [Note that the first three are the same as those in 8.2 above.] 2n−5 (a) 6n−5 (b) (c) (d) ...
