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>
• 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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