Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Math 105A Homework 3
Sumeng Wang
February 18, 2016
2.2.4
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
Sumeng Wang
January 31, 2016
2.1.3
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
Sumeng Wang
February 16, 2016
3.2.3
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 )
.
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
MATH 105A Homework 1
Sumeng Wang
January 20, 2016
Section 1.1.3
2.
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.
There exists