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MathGroup Archive 1998

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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: owner-wri-mathgroup at wolfram.com

Chris wrote:
|
|I'm having trouble with comparisons, see below: |
|In[10]:= x=0.9;
|             y=10;
|
|In[11]:= (1-x)y
|
|Out[11]=1.
|
|The above obviously evaluates to 1. |
|In[12]:= (1-x)y <1
|
|Out[12]= True
|
|The above gives the wrong answer.
|
|In[13]:= (1-x)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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