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MathGroup Archive 2004

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Re: Distinguishable From 1.0

  • To: mathgroup at smc.vnet.net
  • Subject: [mg47729] Re: Distinguishable From 1.0
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Sat, 24 Apr 2004 04:15:25 -0400 (EDT)
  • Organization: Universitaet Leipzig
  • References: <c6aec3$3fe$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

consult 

http://www.library.cornell.edu/nr/bookcpdf/c20-1.pdf

how $MachineEpsilon can be computed and what it mean.

Regards
  Jens


Harold Noffke wrote:
> 
> $Version "5.0 for Microsoft Windows [2000] (November 18, 2003)"
> 
> MathGroup:
> 
> According to MathBook documentation ...
> 
> "$MachineEpsilon gives the smallest machine-precision number which can
> be added to 1.0 to give a result that is distinguishable from 1.0."
> 
> The results below suggest that becoming "... distinguishable from 1.0"
> does not occur until slightly under 1.5 * $MachineEpsilon.
> 
> Is there a misstatement here, or am I misunderstanding something about
> being "... distinguishable from 1.0"?
> 
> In[1]:= 1. + 1.0 * $MachineEpsilon === 1.
> Out[1]= True
> 
> In[2]:= 1. + 1.1 * $MachineEpsilon === 1.
> Out[2]= True
> 
> In[3]:= 1. + 1.2 * $MachineEpsilon === 1.
> Out[3]= True
> 
> In[4]:= 1. + 1.3 * $MachineEpsilon === 1.
> Out[4]= True
> 
> In[5]:= 1. + 1.4 * $MachineEpsilon === 1.
> Out[5]= True
> 
> In[6]:= 1. + 1.5 * $MachineEpsilon === 1.
> Out[6]= False
> 
> Regards,
> Harold


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