# Talk:Oscillation (mathematics)

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Why is it that for 1/x the oscillation is undefined at -∞ and +∞. I would naively think it is zero.67.171.64.190 09:27, 4 June 2007 (UTC)

You are correct. I noticed the same thing. Oleg Alexandrov (talk) 15:28, 4 June 2007 (UTC)

## Another notion of oscillation

There is also another notion -- oscillation of a function (say from a topological space to a metric space) defined by

${\displaystyle \inf\{d(f(U));U{\text{ is an open neighborhood of }}x\}.}$

(It is commonly used that the set of points of discontinuity is a ${\displaystyle G_{\delta }}$ set.) Do we have this notion defined in some other article on wiki? If not, perhaps an article oscillation of a function could be started. --Kompik 10:47, 7 October 2007 (UTC)

(Of course, d(A) in the above definition stands for diameter of a set A.) --Kompik 11:10, 7 October 2007 (UTC)

## is the convergence happened in oscillation

in any oscillating series convergence has happened eg:${\displaystyle 1+(n^{-}n)/n}$

## continuity

In addition to requiring zero oscillation, we need the function to be equal to the limiting value. Since oscillation is defined in terms of liminfs and limsups, apparently the value at the point is ignored. Tkuvho (talk) 07:51, 20 September 2010 (UTC)

I was going to say the same thing. — Preceding unsigned comment added by 186.18.76.220 (talk) 23:03, 23 September 2011 (UTC)

## An equivalent definition is missing

Another definition of oscillation is missing: Let f:I->R (where "I" is an interval contained in R). Then, its oscillation is: supremum(f(I))-infimum(f(I)). 46.19.85.55 (talk) 18:39, 10 August 2014 (UTC)

## same as wave envelope?

merge? Fgnievinski (talk) 00:14, 13 October 2014 (UTC)