CSE
1400
Applied Discrete Mathematics
Theorems
Department of Computer Sciences
College of Engineering
Florida Tech
Spring
2011
1
Theorems
1
1
.
1
Theorems about Arithmetic
1
1
.
2
Theorems about Algebra
2
1
.
3
Theorems about Sets
2
1
.
4
Theorems about Boolean Logic
3
1
.
5
Theorems about Predicate Logic
3
1
.
6
Theorems about Relations
3
1
.
7
Theorems about Functions
3
1
.
8
Theorems about Sequences
4
1
.
9
Theorems about Modular Numbers
4
1
.
10
Theorems about Theorems
4
1
Theorems
Abstract
Theorems are statements that have been proven
True
.
1
.
1
Theorems about Arithmetic
Theorem
1
(Fundamental Theorem of Arithmetic)
.
Every natural
number m greater than
1
is either prime or the product of unique prime
factors.
The order of the prime factors is not
considered important.
Theorem
2
(WellOrdering)
.
Let
X
be a non
empty
subset of the
natural
numbers
. There exists an
element
a
∈
X
such that a
≤
x for all x
∈
X
. This
element a is called the least element of
X
.
Theorem
3
(Archimedean property)
.
For every natural number m there
is a natural number n such that n
>
m.
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View Full Documentcse 1400 applied discrete mathematics
theorems 2
Theorem
4
(QuotientRemainder)
.
Given an
integer
a
∈
Z
and an
integer n
6
=
0
, there exists an integer q and a natural number r, called the
quotient and remainder, such that
a
=
q
·
n
+
r
and
0
≤
r
<

n

.
Theorem
5
(Euclid’s Theorem)
.
There is no largest prime number.
Lemma
1
.
If a
2
is an even integer, then a is even.
Theorem
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 Fall '11
 Shoaff
 Math, Algebra, Natural number, Prime number, Applied Discrete Mathematics Theorems

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