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Re: Distinguishable From 1.0


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


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