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Pi == 3 for imprecise values of 3?

• To: mathgroup at smc.vnet.net
• Subject: [mg22928] Pi == 3 for imprecise values of 3?
• From: Gavin Scott <gscott at netcom.com>
• Date: Thu, 6 Apr 2000 02:04:45 -0400 (EDT)
• Organization: MindSpring Enterprises
• Sender: owner-wri-mathgroup at wolfram.com

In playing with my spiffy new copy of 4.0.2 for Windows, I'm curious
why:

   In[1]:= N[Pi] == 3`0
   Out[1]= True

It seems that a value compared to a number with very low precision
will result in Equal[] returning True.

   In[2]:= 1 == 2`0.00001
   Out[2]= True

   In[3]:= 1 == 2`0.0001
   Out[3]= False

but then

   In[4]:= 10^10 == 2`0
   Out[4]= False

I suppose that when you have zero digits of accuracy then you have no idea
what the value is, so it certainly *could* be equal to any value, but I
find it surprising that == chooses True over False in these cases.

G.