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