Okay, its concerened with michael spivak's book.

there is this one inequality or rather symbol i see, ever since the definition. what exactly does the denote here?? i think it stands for some small distance error, or error in distance towards the y-axis, it does not entirely define what the \epsilon stands for.

also this inequality;

,

i know what the inequality represents but, just dont get the proof provided by the book. The other proofs are alright, though still very challenging indeed.

can anyone explain this concern i have?

thank you