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MathGroup Archive 2004

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RE: SetPrecision - What does in find?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48290] RE: [mg48282] SetPrecision - What does in find?
  • From: "Owen, HL (Hywel)" <H.L.Owen at dl.ac.uk>
  • Date: Sat, 22 May 2004 03:04:21 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Isn't this the same as another recent discussion on Mathematica
representation of numbers? i.e.0.14 is represented in Mathematica as binary, so if
you ask for lots of precision you see the effect of converting it to binary,
truncating to machine precision, and then converting back again to a decimal
display? Is that the right way to think about this?

Hywel

> -----Original Message-----
> From: kazimir04 at yahoo.co.uk [mailto:kazimir04 at yahoo.co.uk]
To: mathgroup at smc.vnet.net
> Sent: 21 May 2004 08:55
> To: mathgroup at smc.vnet.net
> Subject: [mg48290] [mg48282] SetPrecision - What does in find?
> 
> 
> 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?
> 


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