Question

Writing Absolute value can be defined as follows: $\left|a\right|=a\text{if}a\ge 0,\text{and}\left|a\right|=-a\text{if}a<0$. Explain why this definition agrees with the one given at the top of page 23.

Short answer

$\left|a\right|=a\text{if a}\ge 0$

$\left|a\right|=-a\text{if a}<0$.

Step-by-step solution

Step-1 – Concept of integers

Integers include the positive and negative whole numbers including zero. An integer cannot be a decimal or fractional part with it.

The set of integers is denoted by the numbers $...,-4,-3,-2,-1,0,1,2,3,4,...$

Step-2 – Concept of absolute value

The absolute value is defined as the distance of a number from 0 on a number line.

Step-3 – Explanation

For every number mod or absolute value gives the positive terms of that number so when inside the mod number is greater than 0 to do that number positive we take positive sign and when inside the mod number is less than 0 so, to do that number positive and remove the mod we use negative sign and remove the mod.

$\left|a\right|=a\text{if a}\ge 0$

$\left|a\right|=-a\text{if a}<0$