i'm trying to follow this proof of continuity of the function $f(x)=3x+4$ using Delta epsilon.
On minute 5:29, written in green, an inequality suddenly changes to an equality and i'm not sure why.
It would seem that for the definition to hold, you would need $$|f(y)-f(x)|<\epsilon$$ not $$|f(y)-f(x)|=\epsilon$$
And even if that was valid i'm not sure how he got there.
Is this correct? if so why?