what does 2 ideals are equal mean?

Question

I'm revisiting the proof of 1-1 correspondence theorem and while proving $f$ is one-one I don't know how to write mathematically what we mean by 2 ideals are equal? (Here $f$ is a map from set of all ideals of $R$ containing $A$ to set of ideals of $R/A$:= $f(B)=B/A$).

Does equality of 2 ideals means equality element wise . Please help....

$\small($ correspondence theorem is stated as follows: Let A be an Ideal of ring R.There is 1-1 correspondence between Ideals of B containing A and ideals of R/A .$\small)$

Answer 1

Here for simply proving that $f$ is one-one ,you can do this:= $f(B_1)=f(B_2)\implies B_1/A=B_2/A$ $\implies \exists b_1 \in B$ and $b_2 \in B_2$ s.t. $b_1+A=b_2+A$ and then proceed...