# BAD sig from own key

Fri Dec 7 04:03:02 2001

```Last time. Here's the text:

>From cad8@dana.ucc.nau.edu Tue Dec  4 20:59:48 2001
Date: Tue, 4 Dec 2001 20:41:05 -0700 (MST)
To: Anselm Vossen <AnselmV@gmx.de>
Subject: Math

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Checking my answer with you as I go:

1)
a) Not a field, because 2 has no multiplicative inverse.
b) Is a field.

5)
a) Sup: 1, Inf: 0
b) Sup: none, Inf: 0
c) Sup: Pi, Inf: -1

3)
Assume 0 has a mult. inverse, 0^-1
Since F is a field, it has a mult. identity, 1
So, 0 * 0^-1 = 1
But, 0 * x = 0 for all x -> subproof from class notes
So, 0 = 1, which contradicts the fact that F is a field.
So, 0 has no mult. inverse.

4)
a)
Assume x<y
Then x + -x < y + -x
So, 0 < y + -x
So, 0 + -y < y + -y + -x
So, -y < 0 + x
So, -y < -x

b)
Assume x<y and z<0
Then -z exists and
z + -z = 0 < 0 + -z = -z
Since F is an ordered field and x<y and 0<-z, x(-z) < y(-z)
>From problem 2b), -x = (-1)x
So, -z = (-1)z
And x(-1)z < y(-1)z
(-1)xz < (-1)yz
So, xz < yz

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PGP Key ID 0x6550D214
available from:
http://www.keyserver.net

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