/sci/ - Science & Math

>>11492230
In retrospective, there's actually no real reason to define [math]f[/math] if we can't just abridge the whole thing with sequences.
So we get that, for [math]y' \in [ \mathcal{N}_r(x)^c]'[/math] and [math]\epsilon > 0[/math], there's [math] a_{ \epsilon} \in \mathcal{N}_{r}(x)^c [/math] such that [math]a_{ \epsilon} \in \mathcal{N}_{ \epsilon}(y')[/math]. Then [math]||y'-x|| \geq ||x - a_{ \epsilon } || - ||a_{\epsilon} - y'|| \geq r - \epsilon [/math] for any [math]\epsilon > 0[/math].