🔶04 - Theorems of Inequalities and Absolute Value Function

🔶04 - Theorems of Inequalities and Absolute Value Function

In todays video, we are going to discuss the theorems of inequalities as well as the absolute value function

Given that a and b are members of R, then
if a -b is a positive number, then a is either greater than b, or b is less than a, but if there is a possibility that a = b then,
a is greater than or equal to b or b is less than or equal to a

Again if a,b and c are members of R, then
1. either a is greater than b, a = b, or a is less than b - law of trichotomy,
2. if a is greater than b, and b is greater than c, then a is greater than c,
3. if a is greater than b, then a+c is greater than b+c,
4. if a is greater than b and c is greater than 0, then ac is greater than bc,
5. 4. if a is greater than b and c is less than 0, then ac is less than bc

Absolute Value fucntion,
if x is a real number, then
|x| = x if x is positive
|x| = 0 if x is 0
|x| = x if x is negative

eg
|3| = 3
|0| = 0
|-5| = 5

etc

00:00 - Theorems of Inequalities
06:21 - Absolute Value Function
11:13 - Properties of Absolute Value
15:10 - Proof of |xy| = |x||y|
25:15 - Proof of |x/y| = |x|/|y|

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