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}
How clear is this post?