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Distinguishable From 1.0

• To: mathgroup at smc.vnet.net
• Subject: [mg47720] Distinguishable From 1.0
• From: Harold.Noffke at wpafb.af.mil (Harold Noffke)
• Date: Fri, 23 Apr 2004 02:30:50 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

$Version "5.0 for Microsoft Windows [2000] (November 18, 2003)"
Distinguishable From 1.0
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