Re: Re: "Assuming"

*To*: mathgroup at smc.vnet.net*Subject*: [mg85868] Re: [mg85858] Re: "Assuming"*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Tue, 26 Feb 2008 07:43:36 -0500 (EST)*References*: <20080221171506.200$2n_-_@newsreader.com> <200802221221.HAA08545@smc.vnet.net> <200802251237.HAA22859@smc.vnet.net>

Mariano SuÃ¡rez-Alvarez wrote: > On Feb 23, 7:34 am, Daniel Lichtblau <d... at wolfram.com> wrote: > [...] >>[From David Cantrell:] >> >>>>[...] But I do know of a case where >>>>Mathematica goes even further, removing a singularity at which the >>>>function >>>>is defined as a number: >> >>>>In[17]:= FullSimplify[UnitStep[-x^2]] >>>>Out[17]= 0 >> >>>>despite the fact that correctly >> >>>>In[18]:= UnitStep[-x^2] /. x -> 0 >>>>Out[18]= 1 >> >>>>Perhaps the simplification above is considered a bug, perhaps not. >> >>>>David >> >>A feature, really. That is, it's wrong, but FullSimplify can make >>mistakes on measure zero sets. We do not generally regard this >>phenomenon as a bug, though we reconsider on case by case basis. > > > How does that `measure zero' allowance work in a context > of something like > > Assuming[Element[x, Integers], FullSimplify[something]] > > ? > > -- m I've seen cases where the FullSimplify[something] result differs from something on a finite set of integers. This motivated me several months ago to alter assumptions of integrality, to reality (realness? realhood?), in processing of Integrate. Daniel Lichtblau Wolfram Research

**Follow-Ups**:**Re: Re: Re: "Assuming"***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**References**:**Re: "Assuming"***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**Re: "Assuming"***From:*"Mariano Suárez-Alvarez" <mariano.suarezalvarez@gmail.com>