Page 31 - Schaum's Outline of Theory and Problems of Advanced Calculus
P. 31
22 NUMBERS [CHAP. 1
2
1.107. (a)If x is a rational number whose square is less than 2, show that x þð2 x Þ=10 is a larger such number.
(b)If x is a rational number whose square is greater than 2, find in terms of x asmaller rational number
whose square is greater than 2.
1.108. Illustrate how you would use Dedekind cuts to define
p ffiffiffi p ffiffiffi p ffiffiffi p ffiffiffi p ffiffiffi p ffiffiffi p ffiffiffi p ffiffiffi
(a) 5 þ 3; ðbÞ 3 2; ðcÞð 3Þð 2Þ; ðdÞ 2= 3.
