Real Numbers a & b

[nycmathguy]

 

[MathLover1]

|a|-|b|<=|a-b|

You know that |a-b| means the distance between a and b on the number line.
So, you’ve got two points on the number line, a and b .
Picture folding the number line in 1/2 to put the negative side on top of the positive side.
So, what happened? Well, if both a and b were the same sign, their distances didn’t change.
If a and b had opposite signs they just got closer.
Well, when we folded, a went to |a| and b went to |b| . So, now we know that the distance between |a| and |b| might be the same as the distance between a and b or it could be less.

So,
|a|−|b|≤|a−b|

 

[nycmathguy]

|a|-|b|<=|a-b|

You know that |a-b| means the distance between a and b on the number line.
So, you’ve got two points on the number line, a and b .
Picture folding the number line in 1/2 to put the negative side on top of the positive side.
So, what happened? Well, if both a and b were the same sign, their distances didn’t change.
If a and b had opposite signs they just got closer.
Well, when we folded, a went to |a| and b went to |b| . So, now we know that the distance between |a| and |b| might be the same as the distance between a and b or it could be less.

So,
|a|−|b|≤|a−b|

Well-said. To the point! Nice. Cool.