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RE: Comparison Error. Is ther
 To: mathgroup at smc.vnet.net
 Subject: [mg12714] RE: [mg12678] Comparison Error. Is ther
 From: Ersek_Ted%PAX1A at mr.nawcad.navy.mil
 Date: Wed, 3 Jun 1998 02:21:04 0400
 Sender: ownerwrimathgroup at wolfram.com
Chris wrote:

I'm having trouble with comparisons, see below: 
In[10]:= x=0.9;
 y=10;

In[11]:= (1x)y

Out[11]=1.

The above obviously evaluates to 1. 
In[12]:= (1x)y <1

Out[12]= True

The above gives the wrong answer.

In[13]:= (1x)y<1.

Out[13]= False

This gives the right answer, notice the decimal point after the 1. 

In the lines below I present a paradox somewhat related to the problem
above.
First I let (x) be a number near (Pi/2) with eight digits of precision.
In[1]:=
x= 1.57079646`8;
y=Tan[x]
Out[2]=
0. x 10^6
(* Actually that's only the way it looks in a notebook. *)
I think the result in Out[2] means the number is on the order of 10^6,
but the leading digit is unknown. Now you get really strange results
for the tests below.
In[3]:=
x1=6630000;
{x1<r, r<x1}
Out[3]=
{False, False}
In[4]:=
x2=x1+1670000;
{x2<r, r<x2}
Out[4]=
{False, False}
In[5]:=
{
r==x1+100000,
r==x1+200000,
r==x1+300000,
r==x1+400000}
Out[5]=
{True, True, True, True}
What should we get for the results in Out[3], Out[4], Out[5] ? I think
we should get "Uncertain" when two numeric values are compared, and
we can't be certain that the result is True or False.
____________________
Ted Ersek
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