       Re: Why doesn't TrueQ return True here?

• To: mathgroup at smc.vnet.net
• Subject: [mg119752] Re: Why doesn't TrueQ return True here?
• From: Jacare Omoplata <walkeystalkey at gmail.com>
• Date: Mon, 20 Jun 2011 19:37:22 -0400 (EDT)
• References: <itnd1n\$7h2\$1@smc.vnet.net>

```Thanks for the answers. I'll use Simplify in the future. I also
learned that TrueQ is just used to force a True or False answer out.
It gives True when the answer is explicitly true, and gives False in
all other instances. I guess this is useful in programming.

So, if I wanted Mathematica to work on t1 and t2 like real numbers I
should use "\$Assumptions = Element[{t1,t2},Reals]" ?

It does SOMETHING, according to the following output, because Out,
where I've used t1 and t2, is different from Out, where I've used
the undeclared variables s1 and s2.

But it still doesn't give t2-t1 as the answer, but gives Abs[t1-t2]
instead. But I get t2-t1 as the answer in Out and Out, where I
have declared that t2>t1 beforehand.

-----------output-below-------------

In:= \$Assumptions = Element[{t1, t2}, Reals]

Out= (t1 | t2) \[Element] Reals

In:= FullSimplify[Sqrt[(t2 - t1)^2]]

Out= Abs[t1 - t2]

In:= FullSimplify[Sqrt[(s2 - s1)^2]]

Out= Sqrt[(s1 - s2)^2]

In:= \$Assumptions = t2 > t1

Out= t2 > t1

In:= FullSimplify[Sqrt[(t2 - t1)^2]]

Out= -t1 + t2

In:= FullSimplify[Sqrt[(t1 - t2)^2]]

Out= -t1 + t2

In:= \$Assumptions = Element[{t1, t2}, Complexes]

Out= (t1 | t2) \[Element] Complexes

In:= FullSimplify[Sqrt[(t2 - t1)^2]]

Out= Sqrt[(t1 - t2)^2]

In:= FullSimplify[Sqrt[(s2 - s1)^2]]

Out= Sqrt[(s1 - s2)^2]

On Jun 20, 8:05 am, Bob Hanlon <hanl... at cox.net> wrote:
> ??\$Assumptions
>
> \$Assumptions is the default setting for the Assumptions option used in such functions as Simplify, Refine and Integrate.  >>
>
> \$Assumptions=True
>
> TrueQ is not one of the functions that makes use of \$Assumptions.
>
> \$Assumptions = t2 > t1;
>
> Simplify[(t2 - t1) > 0]
>
> True
>
> TrueQ[Simplify[(t2 - t1) > 0]]
>
> True
>
> Bob Hanlon
>
> ---- Jacare Omoplata <walkeystal... at gmail.com> wrote:
>
> =============
> Here's the output.
> -------------------------------------------------------
> In:= Element[{t1, t2}, Reals]
>
> Out= (t1 | t2) \[Element] Reals
>
> In:= \$Assumptions = t2 > t1
>
> Out= t2 > t1
>
> In:= TrueQ[(t2 - t1) > 0]
>
> Out= False
> ------------------------------------------------------
>
> I would expect TrueQ to return True, not False. Why does it return False?
>
> And how can I test whether t2-t1 is positive?
>
> Thanks.

```

• Prev by Date: Re: Only real solutions for a=a^0.7*b
• Next by Date: Re: Why can't FullSimplify give more uniform output?
• Previous by thread: Re: Why doesn't TrueQ return True here?
• Next by thread: Re: Why doesn't TrueQ return True here?