(\mathbb{Q}, +) by |\frac{a}{b}| < 1 a,b\in\mathbb{Z} and b\neq 0 is this a group

by and is this a group.

Identity is 0.

Associative is true.

Inverse (I am not sure but I don't think this works).

If we let be the inverse, we have a problem since

So is this not a group or is this approach to the inverse wrong?

Re: (\mathbb{Q}, +) by |\frac{a}{b}| < 1 a,b\in\mathbb{Z} and b\neq 0 is this a group

Quote:

Originally Posted by

**dwsmith** by

and

is this a group.

Identity is 0.

Associative is true.

Inverse (I am not sure but I don't think this works).

If we let

be the inverse, we have a problem since

So is this not a group or is this approach to the inverse wrong?

Are you asking whether the set is a subgroup of ? Obviously not since .

Re: (\mathbb{Q}, +) by |\frac{a}{b}| < 1 a,b\in\mathbb{Z} and b\neq 0 is this a group

Quote:

Originally Posted by

**Drexel28** Are you asking whether the set

is a subgroup of

? Obviously not since

.

I am trying to prove if it is a group or not.

Re: (\mathbb{Q}, +) by |\frac{a}{b}| < 1 a,b\in\mathbb{Z} and b\neq 0 is this a group

Quote:

Originally Posted by

**dwsmith** I am trying to prove if it is a group or not.

And, it's not since it isn't closed under addition.