Math 105A Homework 3
February 18, 2016
3. If x is a real number, show that there exists a Cauchy sequence of rationals
x1 , x2 , . representing x such that xn < x for all n.
If x Q, we can construct a Cauchy sequence cfw_xn , xn = x. Thi
Math 105A Homework 2
January 31, 2016
1. Show that there is an uncountable number of Cauchy sequences of rational
numbers equivalent to any given Cauchy sequence of rational numbers.
Lets consider the set S = cfw_1, 1, 1, .. S is the set
Math 105A Homework 5
February 16, 2016
1. A is an open set. Show that if a finite number of points are removed from A,
the remaining set is still open.
Assume xi < xj if i < j, A\cfw_x1 , x2 , x3 , ., xk = A(, x1 )(x1 , x2 )(x2 , x3 )
MATH 105A Homework 1
January 20, 2016
a. Every positive integer has a unique prime factorization.
x > 0, x N, x has a unique prime factorization.
Negation: x > 0, x N, x does not have a unique prime factorization.