- #1

mark2142

- 211

- 40

- Homework Statement
- ##|x|<c## is equivalent to ##-c<x<c##

- Relevant Equations
- I tried to understand it by breaking each part.

First lets focus on ##|x|## which is defined as distance between ##x##and ##0##. But if we look into it closely

$$13=|-11-2|$$ which is distance between -11 and 2 but $$13=|11-(-2)|$$ which means this is distance between 11 and -2. Which is it?

In the same way $$x=|x-0|$$ is distance between 0 and x but $$x=|0-(-x)|$$ is distance between 0 and -x. Which is it?

Second lets focus on ##c## which is defined as distance between 0 and c and distance between 0 and -c.

$$|c-0|=c$$ and $$|-c-0|=c$$

##c## mean two things but shouldn't we take one meaning?

Either we take distance between 0 and c or between 0 and -c.

$$13=|-11-2|$$ which is distance between -11 and 2 but $$13=|11-(-2)|$$ which means this is distance between 11 and -2. Which is it?

In the same way $$x=|x-0|$$ is distance between 0 and x but $$x=|0-(-x)|$$ is distance between 0 and -x. Which is it?

Second lets focus on ##c## which is defined as distance between 0 and c and distance between 0 and -c.

$$|c-0|=c$$ and $$|-c-0|=c$$

##c## mean two things but shouldn't we take one meaning?

Either we take distance between 0 and c or between 0 and -c.