From robert Fri May 14 15:15:15 1993
To: adam
Subject: 0=1

Article 7621 of sci.math.symbolic:
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From: wsi@vexpert.dbai.tuwien.ac.at (Wolfgang Slany for Markus Giegl)
Subject: Proof that 0 = 1 in Mathematica 2.0
Message-ID: <1993May14.104113.25642@email.tuwien.ac.at>
Keywords: mathematica
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Date: Fri, 14 May 1993 10:41:13 GMT
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I am posting this for a friend without access to the net. Please reply
by email to me, I will forward it to him. 

(* A proof for 1=0 in Mathematica 2.0 *)
(* You can paste the whole text into Mathematica and start the evaluation 
    in the first line - results will then be output by "Print[]" statements at the end
    of the text *)

(* In[1]: Define the function p(n,x) *)
p[n_,x_]:=n*x^(n-1)     


(* In[2]: Test that p(5,y)=5*y^4. *)
y=.;
Print[];Print["p[5,y]=",p[5,y]]


(* In[3]: Show that the equation 
          d/dx(x*integral(p(n,x)*dx))=d/dx(x*integral(p(m,x)*dx)) 
          holds for n=m, x=1. The internal Mathematica form for an equation of the form "x=y"
          is Equal[x,y]; HoldForm[Equal] prevents Mathematica from trying to evaluate the equation. *) 
          
n=.; m=n; x=.;
a=HoldForm[Equal][D[Integrate[p[n,x],x]*x,x], D[Integrate[p[m,x],x]*x,x]];
x=1; 
Print["equation a for n=m, x=1 gives: ",a]


(* In[4]: Allow Mathematica to evaluate the equation; the result is "True". *)

Print["equation a fully evaluated for n=m, x=1 gives: ",ReleaseHold[a]]


(* In[5]: Calculate the equation for the specific values m=0, n=0; Since above it 
          was shown, that the equation is true for all m=n, this must also be true. *)

n=.; m=0; x=.;
a=HoldForm[Equal][D[Integrate[p[n,x],x]*x,x], D[Integrate[p[m,x],x]*x,x]];
n=0; x=1; 
Print["equation a for m=n=0, x=1 gives: ",a]


(* In[6]: Test that m=n. *)

Print["(Equal[m,n] gives: ",Equal[m,n],")"]


(* In[7]: Test that x=1. *)
Print["(Equal[x,1] gives: ",Equal[x,1],")"]





From robert Sat May 15 14:21:40 1993
To: adam, blackwel@cco, james, phares@romeo
Subject: Mathematica bugs
Cc: robert

I learnt Mathematica on Thursday night, so I decided to use it to do
my math homework =;o)  Here's the first mega-simple integral I tried
it on:

-------------------------------------------------------------------------------
Mathematica 2.0 for SPARC
Copyright 1988-91 Wolfram Research, Inc.
 -- Terminal graphics initialized -- 

In[1]:= Integrate[Exp[I t]^n I Exp[I t],{t,0,2Pi}] 

Out[1]= 0

In[2]:= n=-1

Out[2]= -1

In[3]:= Integrate[Exp[I t]^n I Exp[I t],{t,0,2Pi}] 

Out[3]= 2 I Pi
-------------------------------------------------------------------------------

So 0 = 2 I Pi?  I think not!  Ah well, back to hand calculations...

__robert@vlsi.cs.caltech.edu_____________________________Gonna take you high.__