What is a presentation of a group?

Question

I have read the following:

$\left< a | a^n = 1 \right>$ may be written by $\left< a | a^{n} \right>$ thanks to the convention that terms that do not include an equals sign are taken to be equal to the group identity. Such terms are called relators, distinguishing them from the relations that do include an equals sign.

This paragraph is way too confusing; for example $1$ and $2$ are thus terms without an equal sign in $\mathbb{Z}/3$ how are they equal to the group identity? does anyone have a real definition I can read because I would appreciate it thanks.----

Answer 1

The actual definition of a presentation is that $\left< G\mid R\right>$ stands for the quotient of the free group over the set $G$ quotiented by the normal closure of the set $R$.

The rough definition is that elements of the resulting group are going to be words in the alphabet $G$, subject to the relations present in $R$ (any element of $R$ is set to equal the identity).

Answer 2

for example $1$ and $2$ are thus terms without an equal sign in $\Bbb Z/3$ how are they equal to the group identity?

They're not since they're neither relations nor relators.