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 \(n<m\) then \(n+p<m+p\)
2. if \(n<m\) and \(p<q\) then \(n+p<m+q\)
3. if \(n<m\) and \(p>0\) then \(np<mp\)
4. if \(n<m\) and \(p<0\) then \(np>mp\)
5. if \(0<n<m\) then \(\frac{1}{n}>\frac{1}{m}\)