I am not good at those proofs, and I cannot find any resource because the part of limits is always reduced to the minimum, with few explanations.
$$\lim_{x\to 10} \ln(x - 3) \;=\; +\infty$$
This is clearly false.
$$\forall M > 0, \exists \delta_M > 0 : 0 < |x-x_0|< \delta \implies f(x) > M$$
I am not able to follow this definition to arrive a contradiction, which is what I want.
$f(x) > M$ implies $x > 1 + e^M$.Now I cannot understand how to choose some $\delta$ to show that it's not true that for every $ M > 0$ I have $\ln(x-3) > M$.
How to reason? I don't want to use the negation of the definition.