Re: Lower Floor
- To: mathgroup at smc.vnet.net
- Subject: [mg39030] Re: Lower Floor
- From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
- Date: Sat, 25 Jan 2003 01:24:33 -0500 (EST)
- References: <b0r3j6$4jl$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
"André Giroux" <giroux at dms.umontreal.ca> wrote: > Hi All. > With Mathematica 4.1 on Windows98: > N[Log[8]/Log[2]] > 3. > Floor[N[Log[8]/Log[2]]] > 2 > Beware! I don't find that surprising. After all, you asked for a numerical approximation first! Several comments (based on using version 4.2 for Windows): (1) N[Log[8]/Log[2]] has FullForm 2.9999999999999996`, which, being less than 3, must have its Floor equal to 2 of course. (2) Floor[Log[8]/Log[2]] returns unevaluated, accompanied by a complaint about uncertainty, while Floor[Log[2, 8]] yields 3, just as desire. (3) N[Floor[Log[8]/Log[2]]] evaluates to 2., but again accompanied by a complaint about uncertainty. (Such complaints are valuable.) (4) FullSimplify[Floor[Log[8]/Log[2]]] evaluates to 3, just as we desire. (5) It's simply a bad idea to ask for numerical approximations when you are dealing with something in the vicinity of a jump discontinuity. (Indeed, I think it could be argued that things like Floor[3.] should actually be Indeterminate in Mathematica.) David Cantrell