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SetPrecision - What does in find?

• To: mathgroup at smc.vnet.net
• Subject: [mg48282] SetPrecision - What does in find?
• From: kazimir04 at yahoo.co.uk (Kazimir)
• Date: Fri, 21 May 2004 03:54:30 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Let us run

SetPrecision[.14, \[Infinity]]

MATHEMATICA returns 1261007895663739/9007199254740992. What is the
mathematical (in the sens of mathemaics as a science) reason to give
this answer? I would say that 7/50 is much a better answer.

It looks like that the MATHEMATICA's (in the sens of rules of
MATHEMATICA)  reason 1261007895663739/9007199254740992 can be observed
by the command

N[1261007895663739/9007199254740992, 100]

which answers .14000000000000001332267629550187848508358001708984375000000
00000000000000000000000000000000000000000

It puts 14 zeros after .14 to coinside with 14/100 within the machine
precision which is about 16, than it puts an arbitrary number and than
it puts zeros again. It looks that the number is the exact
presentation of the fractoin 1261007895663739/9007199254740992, but it
is not exactly .14, the deviation being the machine precission.

MATHEMATICA tries to find a fraction which has a finit digital 
presentation, but which defers from the .14 by a michine precision. Is
there a meaning to obtaing a number like this?

• Follow-Ups:
  • Re: SetPrecision - What does in find?
    • From: Daniel Lichtblau <danl@wolfram.com>