Re: Distinguishable From 1.0

*To*: mathgroup at smc.vnet.net*Subject*: [mg47811] Re: Distinguishable From 1.0*From*: ab_def at prontomail.com (Maxim)*Date*: Tue, 27 Apr 2004 04:47:59 -0400 (EDT)*References*: <c6ic20$6j5$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

It gets more interesting if we consider arbitrary-precision numbers: In[1]:= 1`2 == 2.2 1`2 == 2.3 Out[1]= True Out[2]= False If precision of the number 1`2 equals 2 and scale (decimal logarithm of the number) is 0, then accuracy is also 2 and absolute error is 10^-accuracy = 0.01. Then why is this number considered equal to 2.2? Additionally, 1`2-2.2 is converted to machine number, so it is not equal to 0. Also, Equal is not transitive: In[3]:= {99`2 == 0, 0 == -99`2, 99`2 == -99`2} Out[3]= {True, True, False} Looking at RealDigits doesn't clarify things. And another issue: In[4]:= int = Interval[1`2]; IntervalMemberQ[int, 0] IntervalMemberQ[Sin[int], 0] Out[5]= True Out[6]= False If the interval contains the point 0, how can Sin map it to an interval which doesn't include 0? Maxim Rytin m.r at prontomail.com

**Follow-Ups**:**Re: Re: Distinguishable From 1.0***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>