context: currently learning about 'definition of limits' as applied to functions of 2 variables.
$f(x,y)= xy $ consider if: $(x,y)-> (1,2)$
In finding the limit using 'definition of limits'; my notes then write the "statement": $|y|<3$ if $|y-2|<1$.
I agree that the above statement, by itself is correct, however how is it deduced? As in how did the finding of the limit lead to the inferences in the 'statement.'