Modulus

[Jenny4]

Hiya guys, newbie here. I'm really stuck on the following question, so I'd be grateful for any help.

Question:

Let \(\displaystyle x_0 \in R\) and \(\displaystyle \delta>0\). Prove that \(\displaystyle (x_0 - \delta, x_0 + \delta) = \{ x \in R : mod({x-x_0}) < \delta \}\).

My thinking:

I would show working, but I have nothing on my paper I was thinking of squaring \(\displaystyle mod ({x-x_0})\) to get \(\displaystyle +/- (x^2 + (x_0)^2 - 2xx_0) < \delta^2\) but got nowhere. Please help By the way, sorry, I couldn't get the I I mod signs up, so I just typed out mod. I hope you don't confuse this with modulo. My apologies.

Thanks,
Jenny x

 

[royhaas]

On the real line, modulus is the same as absolute value.

 

[Jenny4]

On the real line, modulus is the same as absolute value.

Yes, sorry. I should've used that term. But what should I do?

 

[stapel]

...what should I do?

To show that two sets are equal, one usually shows that each set is a subset of the other. So pick an element in the interval, and show that it is an element of the set. Then pick an element of the set, and show that it is within the interval.

Eliz.

 

[Jenny4]

Thank you, Eliz.