Errata in proof of theorem 2 in chapter 2, limits.html.

[adwaith-pn]

I believe there is an error in the proof of the theorem proving that limits of functions of two real values $(x,y)$.

part of the backward implication of the proof reads:

$\sqrt{(x-x_0)^2 + (y-y_0)^2} = |(x-x_0) + i(y-y_0)| \le |(x+iy)-(x_0+iy_0)|$

though not incorrect mathematically speaking, does the author intend to use "≤" here? Following the use of the triangle inequality in the step prior, I believe this is a typo wherein the corrected version should look like:

$\sqrt{(x-x_0)^2 + (y-y_0)^2} = |(x-x_0) + i(y-y_0)| \le |x-x_0|+|y-y_0|$

If i am mistaken, then the "≤" should be replaced with an "=", as the step only requires variable manipulation.

I've attached the full section from the website below!

do correct me if I'm wrong :))