Algebra - rings $2\mathbb Z$ and $\mathbb Z_3$

Question

Can anyone tell what's the difference between these two rings: $2\mathbb Z$ and $\mathbb Z_3$ ?

I think that ring $2\mathbb Z$ represents remainders when dividing with two, can anyone help? Thanks for your time!

Answer 1

$2\Bbb Z $ is the set of all multiples of $2$ whereas $\Bbb{Z}_3$ is the set of all equivalence classes under the relation $\text{R}$ on $\Bbb Z $ such that $a\text{R}b $ if and only if $3|(b-a) $.

Edit: $\mathbb Z_3$ is also the standard notation for $3$-adic integers.

Courtesy :@rschwieb