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Boundry Pts vs interior points #363

Open bartsnapp opened 5 years ago

bartsnapp commented 5 years ago

I think that every point of the domain is a boundary point, as the domain is a line.

Regardless, I think the nuance of this question is misleading and inappropriate for 2153.

See continuityOfFunctionsOfSeveralVariables/exercises/setClassification2.tex

bartsnapp commented 5 years ago

Hmm... maybe just (8,4) needs to be added to the interior... I'll do this.. but leave this open for later....

NDMathHo commented 5 years ago

(8,4) should be in the interior, but I think I misunderstand the rest of the issue? The domain here is not just a line... I wrote this exercise since there is part of the textbook that addresses classifications of sets in \R^n.

My personal thought is that if we aren't going to appeal to these definitions when we formulate definitions of limits, etc, I don't think this information needs to be in the text and exercises. That being said, it is good "food for thought". In any rate, Math 1172 and 2153 students typically aren't mathematically mature enough to understand the distinction between open sets in R^2 and open sets in the induced topology on the domain of the function...or topological considerations in general. But I don't think this question really gets at more than "If I draw an open ball around the points in question, what points are in it?"

bartsnapp commented 5 years ago

The sole issue was with (8,4). the other stuff was me being confused

NDMathHo commented 5 years ago

No worries. thanks for fixing that problem!