User talk:Ringell

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Cheers! prime mover (talk) 12:42, 21 August 2019 (EDT)

Question about Metric Space Continuity by Open Ball
You added this comment:
 * (*) Only consider this case, since otherwise $\map {d_1} {x, a} < \delta \implies \map {d_2} {\map f x, \map f a} < \epsilon$ is vacuously true.

I don't understand. What the proof is purporting to do is demonstrate that, given $\map {d_1} {x, a} < \delta$, it can be proved that $\map {d_2} {\map f x, \map f a} < \epsilon$.

That is accomplished by the 3 lines given; that being done, the proof is complete.

What is the "otherwise"?

Also note that the extra lines of clarification at the start of the proof do nothing more than merely restate exactly what has been stated at the top of each section, so I need to be convinced that we need to keep them. --prime mover (talk) 08:11, 30 November 2020 (UTC)