       Re: Equality question

• To: mathgroup at smc.vnet.net
• Subject: [mg29554] Re: Equality question
• From: "Orestis Vantzos" <atelesforos at hotmail.com>
• Date: Sun, 24 Jun 2001 22:10:13 -0400 (EDT)
• Organization: National Technical University of Athens, Greece
• References: <9h3vmg\$46c\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```The bottom line being...TrueQ does not use any "mathematical" information
about its argument - it checks the truth of its argument in a "programming"
sense, more or less.
Simplify on the other hand does the opposite - it uses all mathematical
knowledge available to reduce the expression to a simpler form - usually
True or False for equations.
Orestis

Andrzej Kozlowski" <andrzej at tuins.ac.jp> wrote in message
news:9h3vmg\$46c\$1 at smc.vnet.net...
> on 6/23/01 2:47 PM, gleam at flashmail.com at gleam at flashmail.com wrote:
>
> > Hi, I'm new to this mailing list, and rather new to Mathematica.
> >
> > Why doesn't Mathematica 4.1 yield True for this expression:
> >
> > TrueQ[(n - 1)^2 + n == n^2 - n + 1]
> >
> >
> >
> The way to check if such an expression is True or False is:
>
> In:=
> Simplify[(n - 1)^2 + n == n^2 - n + 1]
>
> Out=
> True
>
> The Predicate TrueQ is not meant for such purposes.It does not in itself
> invoke any simplifications because if it did it would be inconvenient to
use
> it programs where you want the expression TrueQ[x] to remain unevaluated.
> Also for programming reasons all Mathematica predicates which do not
return
> True return False (even though that might look like a false answer!). In
the
> case of very simple expresion Mathematica will perform simplifications
> without the use of Simplify, and in such cases applying TrueQ will yield
> True because in any case the  result of the evaluation was True before
TrueQ
> was applied, e.g:
>
> In:=
> TrueQ[n + 1 + 1 == n + 2]
>
> Out=
> True
>
> because
>
> In:=
> n + 1 + 1 == n + 2
>
> Out=
> True
>
> On the other hand in your case:
>
> In:=
> (n - 1)^2 + n == n^2 - n + 1
>
> Out=
>         2                 2
> (-1 + n)  + n == 1 - n + n
>
> Mathematica does not simplify this expression (without applying Simplify),
> so TrueQ, which must return True or False has to return False. It does
look
> strange, but that is because Mathematica's predicates are not meant to
serve
> the purpose of "answering a question", which beginners sometimes assume
them
> to be for
> e.g.
>
> In:=
> IntegerQ[(1 + Sqrt)^2 - 1 - 2*Sqrt]
>
> Out=
> False
>
> but are intended for writing fucntions of the kind
>
> If[IntegerQ[x], ....]
>
> and so on.
>
>
> I hope this is clear enough.
>
>
> --
> Andrzej Kozlowski
> Toyama International University
> JAPAN
>
> http://platon.c.u-tokyo.ac.jp/andrzej/
> http://sigma.tuins.ac.jp/~andrzej/
>
>
>
>
>

```

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