Things that I learnt today. Emphasis on the I, I couldn’t make for MAM1000W today.

• Absolute value definition
• Properties of absolute values
• Rules for inequalities

Absolute value

The absolute value of a number represents the distance between that number and $0$ on the real number line. Absolute value of a number $n$ is denoted by $|n|$ which is equal to $\sqrt{n^{2}}$ which is from the distance formula. Since it is the distance between $0$ and $n$ Hence $|n|=n$ if $n \geq 0$ and $|n|=-n$ if $n < 0$

Properties of Absolute values

1. $|nm| = |n||m|$
2. $|\frac{n}{m}| = \frac{|n|}{|m|}, (m \neq 0)$
3. $|n^{m}| = |n|^{m}$

Let $n > 0$ then

1. $|m| = n \iff m = \pm{n}$
2. $|m| < n \iff -n < m < n$
3. $|m| > n \iff m > n, m < -n$

Rules for inequalities

1. if $n then $n+p
2. if $n and $p then $n+p
3. if $n and $p>0$ then $np
4. if $n and $p<0$ then $np>mp$
5. if $0 then $\frac{1}{n}>\frac{1}{m}$
 How clear is this post?