Algebra beginning with A

Algebraic Terms
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Absolute Value

The value of the number, ignoring the positive or negative sign. Symbolically, it is referenced by placing vertical bars on the left and right of the number.

|3| = 3
|-3] = 3
Additive Identity

The number zero (0), the number that can be added to any other real number and not change the number.

Let A be real numbers,
then
  0 + A = A is the additive identy.

0 + 5 = 5
0 + 11 = 11
0 + c = c
Axiom: Additive Inverse

Let A be a real numbers,
then
  -A is the additive inverse and A + (-A) = 0

Given 3, -3 is the additive inverse because 3 + (-3) = 0
Axiom: Associative Property of Addition

Let A, B and C be real numbers,
then
  (A + B) + C = A + (B + C)

(2 + 3) + 5 = 2 + (3 + 5)
(5 + 4 ) + 10 = 5 + (4 + 10)
Axiom: Associative Property of Multiplication

Let A, B and C be real numbers,
then
  A x (B x C) = (A x B) x C

2 x (5 x 3) = (2 x 5) x 3
11 x (2 x 3) = (11 x 2) x 3
Axiom: Closure in Addition

Let A and B be real numbers,
then
  A + B is a real number

99 + 22 = 121
14 + 30 = 44
1/2 + 1/2 = 1
0.12 + 1.23 = 1.35
Axiom: Closure in Multiplication

Let A, B and C be real numbers,
then
  A x B is a real number

2 x 3 = 6
9 x 3 = 27
1/2 x 2/3 = 1/3
2 x 0.1 = 0.2
Axiom: Commutative Property of Addition

Let A and B be real numbers,
then
  A + B = B + A

2 + 3 = 3 + 2
11 + 9 = 9 + 11
Axiom: Commutitive Property of Multiplication

Let A and B be real numbers,
then
  A x B = B x A

5 x 3 = 3 x 5
11 x 7 = 7 x 11
Axiom: Multiplicative Identy

The value 1, the number that multiplies times any other number and does not change the value.

Let A be real numbers,
then
  1 is the identity
  because 1 x A = A

1 x 8 = 8
17 x 1 = 17
1 x M = M
Axiom: Multiplicative Inverse

Let A be a real numbers,
then
  1/A is the multiplicative inverse
  because A x 1/A = 1.

Given 2, the multiplicative inverse is 1/2.
2 x 1/2 = 1

Given 1/3, the multiplicative inverse is 3.
1/3 x 3 = 1

Given 17, the multiplicative inverse is 1/17.
17 x 1/17 = 1

Given a, the multiplicative inverse is 1/a.
a x 1/a = 1