Talk:Classification of discontinuities

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===Better to classify like this:

==1) Removable

==2) Essential ... which have the following sub classifications....

=2a) (Finite) Jump =2b) Infinite (Jump) =2c) Oscillatory

==1) means... limit exists.... but not equal to function value

==2) means....limit does not exist

=2a) limit does not exist because the left and right limits (which exist and are finite) are not equal =2b) limit does not exist because left and/or right limit is +/- infinity =2c) limit does not exist because of oscillatory action near point --anon

I don't think that a finite jump discontinuity is an "essential discontinuity". Do you have references for that? Oleg Alexandrov (talk) 13:59, 15 May 2006 (UTC)

(Finite) Jump Discontinuities are essential because the criteria to determine if a discontinuity is essential or not is whether the limit exists at the point. Of a function has a finite jump, the limit does not exist there (left and right limits are unequal), thus there exists an essential discontinuity there.

here is the first link I clicked after searching for essential disc http://oregonstate.edu/instruct/mth251/cq/Stage4/Lesson/jumps.html

Unfortunately, this use of essential clashes with the use of essential singularity in complex analysis. The same goes for the article, by the way. Another possible point of confusion with the classification in the article is that "not removable" and "non-removable" are not the same. -- Jitse Niesen (talk) 02:55, 17 May 2006 (UTC)

[edit] Confusion

This article was confusing continuous functions (which are continuous on their domains) with continuous funciton on the real numbers. So technically all the example functions are continuous if they are not defined at x=1. I have edited the examples so that they are all total functions, removing this confusion. I would like to make the jump discontinuity half-continuous but then I would have to edit the image. —The preceding unsigned comment was added by 2006 80.57.33.218 (talk • contribs) .

You are right of course. I did not think of that when i added the examples. Oleg Alexandrov (talk)