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