Homework 2  Math 139
Due Sep 13th
Instructor
Mauro Maggioni
Office
293 Physics Bldg.
Office hours
Monday 1:30pm3:30pm.
Web page
www.math.duke.edu/˜mauro/teaching.html
Reading
: from Reed’s textbook: Sections 2.1,2.2
Problems
:
§
1.1: #8, 10, 11 (in these problems assume only that
x
and
y
are elements of an ordered
field
F
; in #11 assume in addition that
F
is Archimedean. In the hint for #11, use the
wellordering principle to show that
m
exists)
§
1.4: #9, 11 (You don’t need
a.
to do
c.
; try using
b.
and #11 above)
Additional Problems:
1
.
Prove that the field
C
of complex numbers cannot be given the structure of an
ordered field. (
Suggestion:
Argue by contradiction: suppose a subset
P
⊆
C
exists with
the required properties; then
i
∈
P
∪
(

P
), where
i
is the complex number such that
i
2
=

1. Deduce the contradiction from this.)
2
..
Let
F
be a field.
Prove that if there is an integer
n
∈
N
such that 1 + 1 +
· · ·
+
1 (
n
terms) = 0, then there is no subset
P
⊆
F
saisfying the axioms of an odered field.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 Pardon,W
 Math, Web page, Natural number, Archimedean, Mauro Maggioni

Click to edit the document details