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Transcript 
Axioms for Addition
Properties for Addition
The CLOSURE property for Addition
For all real numbers a and b :
a  b is a unique real number
a , b , ! c ;(a  b  c)
The ASSOCIATIVE property for Addition
For all real numbers a, b, and c:
a b c  a  b c
The COMMUTATIVE property for Addition
For all real numbers a and b:
a b  ba
a , b ; a  b  b  a
IDENTITY Property of Addition
(0 is the Additive Identity)
There is a unique real number 0 such that for
every real number a,
a  0  a and 0  a  a .
a ; (a  0  a)  0  a  a
b g b g
a, b, c ; b
a  bg
c  a b
b  cg
b
Property of OPPOSITES
g
For every real number a , there is a unique real
number a such that
a  a  0 and a  a  0
bg
a , !(a);
bg
(a  b
ag
 0)  c
bag a  0h
Definition of Subtraction
Definition of Subtraction
For all real numbers a and b , the difference a - b is defined by
a  b  a  b
to subtract b, add the opposite of b.
a, b ; a  b  a  b
bg
bg
1
add_prop.doc
4/30/2017
Axioms for Addition
Sample Quiz on Axioms for Addition
1. Find a solution set for x  4  7
x4  7
x  4  4  7  4
x  4  4  7  4
b g
b g
Given
x  0  7  4
x  7  4
x3
2. Find a solution set for x  3  7
Given
x3 7
x  3  7
x  3  3  7  3
b g
x b
3  3g
 73
x0 73
x  73
x  10
3. Find a solution set for x  4  3
Given
x  4  3
x  4  3
x  4  4  3  4
x  4  4  3  4
b g
b g
x  0  3  4
x  3  4
x 1
4. Find a solution set for 3  x  1
Given
3  x  1
x  3  1
x  3  3  1  3
x  3  3  1  3
b g
b g
x  0  1  3
x  1  3
x2
2
add_prop.doc
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Axioms for Addition
5. Find a solution set for 3  2  x
Given
3  2  x
2  x  3
x  2  3
x  2  2  3  2
x  2  2  3  2
b g
b g
x  0  3  2
x  3  2
x  1
Quiz on Axioms for Addition
1. Find a solution set for x  4  7
x4  7
x  4  4  7  4
x  4  4  7  4
b g
b g
Given
x  0  7  4
x  7  4
x3
2. Find a solution set for x  3  7
Given
x3 7
x  3  7
x  3  3  7  3
x  3  3  7  3
b g
b g
x0 73
x  73
x  10
3. Find a solution set for x  4  3
Given
x  4  3
x  4  3
x  4  4  3  4
x  4  4  3  4
b g
b g
x  0  3  4
x  3  4
x 1
3
add_prop.doc
4/30/2017
Axioms for Addition
4. Find a solution set for 3  x  1
Given
3  x  1
x  3  1
x  3  3  1  3
b g
x b
3  3g
 1  3
x  0  1  3
x  1  3
x2
5. Find a solution set for 3  2  x
Given
3  2  x
2  x  3
x  2  3
x  2  2  3  2
b g
x b
2  2g
 3  2
x  0  3  2
x  3  2
x  1
4
add_prop.doc
4/30/2017
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