This preview shows pages 1–2. Sign up to view the full content.
MAE3811–Sp. 2010 Mahoney–1
Division for the Integers
It is defined exactly the same as it was for whole numbers
WHOLE #:
Formally, for any whole numbers
a
and
b
, with
b not equal to 0
,
a ÷ b = c
if and only if
c
is the
unique
whole number such that
b∙c = a
.
INTEGERS:
Formally, for any integers
a
and
b
, with
b not equal to 0
,
a ÷ b = c
if and
only if
c
is the
unique
whole number such that
b∙c = a
.
So what’s the difference in the definitions?
Examples:
12 ÷

4

12 ÷ 4

12 ÷

4

12 ÷

5
MAE3811–Sp. 2010 Mahoney–2
Ordering of the Integers
It is defined exactly the same as it was for whole numbers
Whole: Definition of Less Than:
For any whole numbers a and b, a is
strictly less
than b, written a < b, if, and
only if, there exists a natural number k such that a + k = b
Integer: Definition of Less Than:
For any integers a and b, a is
strictly less
than b, written a < b, if, and only if,
there exists a positive integer k such that a + k = b
So what’s the difference in the definitions?
Theorem: a < b (or b > a) if
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '11
 Mahoney

Click to edit the document details