Question

what is the definition of group?

Answer 1

Group is an algebraic structure consisting of a set of elements together with an operation that combines any two elements to form a third element.
https://en.wikipedia.org/wiki/Group_(mathematics)

Answer 2

no

Answer 3

A group is a set G with an operation * s.t.

1) there is an element e s.t. g*e = g for all g in G
2) for all g in G there is an element g^-1 s.t. g*g^-1 = g^-1*g = e
3) for all a,b in G a*b is in G


So For the natural number \(\mathbb{N}=\{1,2,3,4,5,...\}\) and addition \(+\) look at number 2)

Consider \(2\in \mathbb{N}\). Is there a natural number s.t. when added to \(2\) you get \(0\) (\(0\) is e from 1))

Answer 4

.