# Two inequalities help

1. Aug 22, 2010

### annoymage

1. The problem statement, all variables and given/known data

$$||a|-|b||\leq{i don't know from here}\leq|a|-|b|\leq|a-b|$$

2. Relevant equations

n/a

3. The attempt at a solution

help

2. Aug 22, 2010

### hunt_mat

Re: inequality

You should know that:
$$|x+y|\leqslant |x|+|y|$$
So, we can write:
$$|x|=|x-y+y|\leqslant |x-y|+|y|$$
Likewise
$$|y|=|y-x+x|\leqslant |x-y|+|x|$$

3. Aug 22, 2010

### annoymage

Re: inequality

i knoe, but that would only answer this
$$|a|-|b|\leq|a-b|$$

but this one, is it related? i can't see T_T
$$||a|-|b||\leq|a-b|$$

4. Aug 22, 2010

### hunt_mat

Re: inequality

it shows that:
$$|a|-|b|\leqslant |a-b|$$
and
$$-(|a|-|b|)\leqslant |a-b|$$

5. Aug 22, 2010

### hunt_mat

Re: inequality

finally the penny drops. This is why I recommended the analysis books!!!

6. Aug 22, 2010

### annoymage

Re: inequality

i still, like structure more than limit tough, maybe the reason i dislike analysis NOW(maybe later i love it more) because now i'm studying calculus and some methodS, too much memorizing, not vigorous at all, which despise me. ngahaha

7. Aug 22, 2010

### hunt_mat

Re: inequality

Give it time to internalise. Analysis was my first love in maths