piecewise and if

*To*: mathgroup at smc.vnet.net*Subject*: [mg128622] piecewise and if*From*: Jon Joseph <josco.jon at gmail.com>*Date*: Sat, 10 Nov 2012 02:08:52 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

I think these two functions should be the same but their plots show a clear difference: f[x_, y_] := Exp[-1/(x^2 + y^2)] (* this function undefined at (0,0) *) g[x_, y_] := Piecewise[{{0, x == 0 && y == 0}}, f[x, y]] (* Redefine so the hole is plugged *) h[x_, y_] := If[x == 0 && y == 0, 0, f[x, y]] (* Another, I think, equivalent way to redefine f[x, y] *) On my machine, "8.0 for Mac OS X x86 (64-bit) (October 5, 2011)" when I Plot3D[g[x, y], {x, -1,1}, {y, -1,1}] Plot3D[h[x, y], {x, -1,1}, {y, -1,1}] I see clear gaps along y=0 and x=0 for the g[x, y] plot and h[x, y] works properly. Am I misusing Piecewise? Thanks, Jon.

**Follow-Ups**:**Re: piecewise and if***From:*Bob Hanlon <hanlonr357@gmail.com>

**Re: piecewise and if***From:*Bob Hanlon <hanlonr357@gmail.com>