1. ## Inequality Prove

Show that for all real numbers a and b,
we have | a | - | b | less than or equal to | a - b |.

The hint given in the textbook tells me to begin with the identity a = (a - b) + b, then take the absolute value of each side and finally use the triangle inequality.

2. ## Re: Inequality Prove

Can you show us what you have tried?

3. ## Re: Inequality Prove

Originally Posted by chiro

Can you show us what you have tried?
Can this be proven by setting a and b to equal any integer?

4. ## Re: Inequality Prove

Can this be proven by setting a and b to equal any integer?
NO! Nothing is ever proved by example.
You say that you understand the triangle inequality.
\displaystyle \begin{align*}|a|&=|a-b+b| \\&\le|a-b|+|b|\\|a|-|b|&\le |a-b| \end{align*}

You write back and explain those steps.

5. ## Re: Inequality Prove

Originally Posted by Plato
NO! Nothing is ever proved by example.
You say that you understand the triangle inequality.
\displaystyle \begin{align*}|a|&=|a-b+b| \\&\le|a-b|+|b|\\|a|-|b|&\le |a-b| \end{align*}

You write back and explain those steps.
You are saying to replace every "a" with (a - b) + b and simplify.

6. ## Re: Inequality Prove

You are saying to replace every "a" with (a - b) + b and simplify.
Why are you doing this to yourself?
You clearly don't have any idea what its is all about.
Do you even have the intellectual background to know what a proof is?

7. ## Re: Inequality Prove

Originally Posted by Plato
Why are you doing this to yourself?
You clearly don't have any idea what its is all about.
Do you even have the intellectual background to know what a proof is?
I am trying to learn.

8. ## Re: Inequality Prove

Originally Posted by Plato
NO! Nothing is ever proved by example.
It is standard practice to use a counterexample to disprove something if it is false.

9. ## Re: Inequality Prove

Originally Posted by greg1313
It is standard practice to use a counterexample to disprove something if it is false.
To disprove is not to prove. Is English your native language?
None can prove a negative, one only offers a counterexample.

10. ## Re: Inequality Prove

Originally Posted by Plato
To disprove is not to prove.
Incorrect. To disprove is to prove a claim or an assertion is false.

some sites:

Originally Posted by Plato
It certainly is. From your ignorance of the meaning, maybe it isn't your native language.
Either way, you need to stop hostile attitudes by not addressing me with a question like that.
It crosses a line.

Originally Posted by Plato
None can prove a negative, one only offers a counterexample.
Wrong, of course one can prove a negative. Just for a major example, Andrew Wile
proved Fermat's Last Theorem. Andrew Wile proved a negative.

11. ## Re: Inequality Prove

Originally Posted by greg1313
Either way, you need to stop hostile attitudes by not addressing me with a question like that.
It crosses a line
I have never considered correcting ignorance as crossing a line.
It is perfectly clear to me that you have never done any active research in proof theory.
What else could explain your not knowing what proving a negative means?
You are full-of-yourself having two posts as opposed to twenty thousand.

12. ## Re: Inequality Prove

Originally Posted by Plato
I have never considered correcting ignorance as crossing a line.

It is perfectly clear to me that you have never done any active research in proof theory.
What else could explain your not knowing what proving a negative means?
You are full-of-yourself having two posts as opposed to twenty thousand.
It's clear you never corrected me in the first place. You display a hostile attitude with me (and also that you show in many other posts with many other users). That is separate from correcting someone.
Either way, your unprovoked hostility is not justified. You shouldn't be judging anyone about proof theory when you can't get it right. It is irrelevant as to how many posts I have here. That doesn't even make sense. I am not "full-of-myself." I am anti-arrogant.

And now I will start combing through some of your other posts for errors.

13. ## Re: Inequality Prove

I should say that the only questions you will ever see from me are textbooks problems that I couldn't solve after several tries. I don't just try to solve a problem once and then give up. I go at it several times and sometimes for several days in my study room, covering every possible approach.

From now on I will show my work or effort. I am not seeking a complete solution but hints leading to a solution to all questions posted. Math is fun. This group is fun.

There is no need for insulting words and senseless arguments. No one in this group knows all there is to know about math or any other subject. If my questions and posts upset certain members, you have a choice to skip and/or ignore.