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a workaround could be to delete just the entries of DownValues
which contain the symbol u.

To demonstrate I add to your]]> May 21, 2012 5:59:07 AM May 21, 2012 5:59:07 AM christoph.lhotka@fundp.ac.be 0 http://mathforum.org/kb/thread.jspa?messageID=7826118&tstart=0#7826118 ]]> May 21, 2012 5:59:06 AM May 21, 2012 5:59:06 AM 1 http://mathforum.org/kb/thread.jspa?messageID=7825672&tstart=0#7825672
> Hi !
> Here is something very simple I don't understand :
>
> f[x_] := x;]]> May 20, 2012 2:34:56 AM May 20, 2012 2:34:56 AM phbrf@t-online.de 0 http://mathforum.org/kb/thread.jspa?messageID=7825315&tstart=0#7825315
>Hi ! Here is something very simple I don't understand]]> May 19, 2012 5:47:06 AM May 19, 2012 5:47:06 AM readnews@sbcglobal.net 0 http://mathforum.org/kb/thread.jspa?messageID=7825326&tstart=0#7825326 > Hi !
> Here is something very simple I don't understand]]> May 19, 2012 5:44:02 AM May 19, 2012 5:44:02 AM awnl@gmx-topmail.de 0 http://mathforum.org/kb/thread.jspa?messageID=7824932&tstart=0#7824932 Hi !
Here is something very simple I don't understand :

f[x_] := x; f[2] (*A function*)
2

Clear[f]; f[2] (*The same]]> May 18, 2012 5:27:53 AM May 18, 2012 5:27:53 AM ahautot@ulg.ac.be 5