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Re: More /.{I->-1} craziness

  • To: mathgroup at smc.vnet.net
  • Subject: [mg106530] Re: More /.{I->-1} craziness
  • From: AES <siegman at stanford.edu>
  • Date: Fri, 15 Jan 2010 03:20:58 -0500 (EST)
  • Organization: Stanford University
  • References: <hhhme6$o0s$1@smc.vnet.net>

In article <hhhme6$o0s$1 at smc.vnet.net>, Bob Hanlon <hanlonr at cox.net> 
wrote:

> You appear to be comparing apples and oranges.
> 
> Head /@ {I, E, Pi, Infinity}
> 
> {Complex,Symbol,Symbol,DirectedInfinity}
> 
> FullForm /@ {I, E, Pi, Infinity}
> 
> {Complex[0,1],E,Pi,DirectedInfinity[1]}
> 
> Since rules are applied to the FullForm,,,
> 
> 
> Bob Hanlon

Responses to this and many other similar responses in this thread:  

1)  The problem is not explaining _why_ or _how_ this behavior 
happens; the problem is that Mathematica has been constructed 
_so that it happens_ --  and it's a damaging and unfortunate
and undesirable (and, at base, unnecessary?) way for Mathematica to 
respond.

In other words, it's not necessarily a "bug" -- I don't have an opinion, 
or even qualifications to have an opinion, on that point -- but it's 
certainly a product defect..

2)  Quote from the primary Help for I:

"The symbol I needs to be evaluated to become a complex number:"

Huh?  What?  "The **symbol** I ...?"

How many ordinary users of Mathematica do you think would view I, E and 
Pi as symbols that all happen to represent a number -- but that all 
function as symbols until you call for a numerical output?

Put another way, how many users do you think would automatically know or 
expect, from their pre-Mathematica eduction that I, E and Pi would be 
handled in this different (inconsistent) way in Mathematica?


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