Finding the Truth Set of a Predicate: 1 <= x^2 <= 4, domain: Z

[mr_coffee]

Hello everyone!

I was wondering if someone could check to see if i did this problem correctly.

THe directions are the following: Fid the truth set of each predicate.
predicate: 1 <= x^2 <= 4, domain: Z. Where Z stands for integers and <= stands for less than or equal to.

The book did an example of the following:
predicate: 1 <= x^2 <= 4, domain: R.
There answer was:
The truth set is the set of all real numbers x, with the properlty that 1 <= x^2 <= 4, so the truth set is {x e R|-2 <= x <= -1 or 1 <= x <= 2 }. In other words, the truth set is the set of all real numbers between -2 and -1 inclusive and between 1 and 2 inclusive.


Now for my problem, wouldn't the answer be the exact same thing but instead write:
The truth set is the set of all real numbers x, with the properlty that 1 <= x^2 <= 4, so the truth set is {x e Z|-2 <= x <= -1 or 1 <= x <= 2 }. In other words, the truth set is the set of all integers between -2 and -1 inclusive and between 1 and 2 inclusive.

note: e stands for element of. I need to find the latex for all this so it will be clearer.

Whats the major difference between real numbers and integers anyways?

Thanks! :D

 

[0rthodontist]

Well, your approach is technically correct, but you shouldn't leave it like that. The integers is the set of numbers with no fractional part:
{... -3, -2, -1, 0, 1, 2, 3, 4, ...}
The real numbers is the set of numbers that can be represented by an infinite decimal expansion, like 12, 1.9, 1.37373737..., or pi.

So you have the set of all integers between -2 and -1 inclusive or between 1 and 2 inclusive. Can you actually name those integers?

 

[mr_coffee]

So i could just write:
The truth set is the set of all real numbers x, with the properlty that 1 <= x^2 <= 4, so the truth set is {x e Z|-2 <= x <= -1 or 1 <= x <= 2 }. In other words, the truth set is the set of all integers between -2 and -1 inclusive and between 1 and 2 inclusive. i.e. {-2,-1,1,2} Why isn't 0 included in the integer set?
Thanks for the help! :)edit: is 0 not included because it makes the predicate false? becuas if u plug in 0 for x, 0 is not less than or equal to 1 or less than or equal to 4

 

[0rthodontist]

Right, {-2, -1, 1, 2}.

 

[mr_coffee]

thanks again!