(related to Proposition: Limit of the Constant Function)
- Let $c\in\mathbb R$ and let $a\in\mathbb R.$
- Let $f:\mathbb R\to\mathbb R,$ $f(x)=c$ be the constant function.
- Then for $\delta:=\epsilon$ we have that for all $x$ with $0 < |x-a| < \delta$ we have that $|f(x)-c|=|c-c|=0 < \epsilon.$
Thank you to the contributors under CC BY-SA 4.0!
- Kane, Jonathan: "Writing Proofs in Analysis", Springer, 2016