Can sage help determine if $|f(x) - L| < \epsilon$ is true?
Here's what I want to check:
Given $f(x)$, $\epsilon>0$, $L\in \mathbb{R}$ and $N(\epsilon)$, is $$n>N(\epsilon) \Rightarrow |f(n)-L | < \epsilon$$ true?
I thought I could accomplish this using symbolic expressions and assume(). This is what I've tried:
forget()
var('ep, n')
f(x)=1/(n+7)
N = (1/ep)-7
assume(ep>0)
assume(n>N)
show(abs(f(n)-0)<ep)
bool(abs(f(n)-0)<ep)
But the result of is False. What is the proper way to do this in Sage?
Edited: "< epsilon" instead of "< 3" in the displayed equation. Also, you want f(x) = 1 / (x + 7), not 1 / (n +7).