# Thread: The Set of Irrational Numbers and Groups

1. ## The Set of Irrational Numbers and Groups

Can the set of all irrational numbers with operation addition be considered a group?

2. Originally Posted by MissMousey
Can the set of all irrational numbers with operation addition be considered a group?

And what would the unit element be?....

Tonio

3. Originally Posted by tonio
And what would the unit element be?....

Tonio
I don't know. I mean, 0 isn't an irrational number so it doesn't belong to the set of irrational numbers.

...maybe I can just say that since this set doesn't contain an identity element, it is not a group....right?