Definition talk:Continuous Mapping (Metric Space)/Point

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I'm just wondering what the reasons are as to why this definition is chosen as "the definition". I think it's kind of strange to distinguish between limit points and other points when defining continuity, since it isn't necessary. Any comments? --abcxyz (talk) 03:22, 13 October 2012 (UTC)

Probably because it was an extrapolation from the definition on the real number line. Shrug. If someone wants to completely refactor this area I won't stop them as long as they're careful.
I don't understand what you mean by "to distinguish between limit points and other points" - where precisely is this done? It just mentions $a$ and then the condition that the limit of $f(x)$ equals $a$. It doesn't distinguish between the limit-ness of either point, in that it says "$x$ is not a limit point" - or what was it you meant? --prime mover (talk) 07:10, 13 October 2012 (UTC)
Currently, the limit is only defined if $a$ is a limit point of $A_1$. --abcxyz (talk) 12:41, 13 October 2012 (UTC)