Re: Why doesn't TrueQ return True here?

*To*: mathgroup at smc.vnet.net*Subject*: [mg119764] Re: Why doesn't TrueQ return True here?*From*: Jacare Omoplata <walkeystalkey at gmail.com>*Date*: Tue, 21 Jun 2011 05:52:10 -0400 (EDT)*References*: <itnd1n$7h2$1@smc.vnet.net> <itoljh$eqh$1@smc.vnet.net>

OK, now that I'm reading what I've posted yesterday, it makes no sense, I guess because I was practically dozing in my chair when I wrote that. Of course, Mathematica gave Abs[t1-t2] as the answer because it didn't know which one was greater. When it had the information that t2>t1, it evaluated Abs[t1-t2] and returned t2-t1 . Sorry about that stupid mistake. On Jun 20, 7:37 pm, Jacare Omoplata <walkeystal... at gmail.com> wrote: > 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[3], > where I've used t1 and t2, is different from Out[4], 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[6] and Out[7], where I > have declared that t2>t1 beforehand. > > -----------output-below------------- > > In[1]:= $Assumptions = Element[{t1, t2}, Reals] > > Out[1]= (t1 | t2) \[Element] Reals > > In[3]:= FullSimplify[Sqrt[(t2 - t1)^2]] > > Out[3]= Abs[t1 - t2] > > In[4]:= FullSimplify[Sqrt[(s2 - s1)^2]] > > Out[4]= Sqrt[(s1 - s2)^2] > > In[5]:= $Assumptions = t2 > t1 > > Out[5]= t2 > t1 > > In[6]:= FullSimplify[Sqrt[(t2 - t1)^2]] > > Out[6]= -t1 + t2 > > In[7]:= FullSimplify[Sqrt[(t1 - t2)^2]] > > Out[7]= -t1 + t2 > > In[10]:= $Assumptions = Element[{t1, t2}, Complexes] > > Out[10]= (t1 | t2) \[Element] Complexes > > In[11]:= FullSimplify[Sqrt[(t2 - t1)^2]] > > Out[11]= Sqrt[(t1 - t2)^2] > > In[12]:= FullSimplify[Sqrt[(s2 - s1)^2]] > > Out[12]= 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[29]:= Element[{t1, t2}, Reals] > > > Out[29]= (t1 | t2) \[Element] Reals > > > In[30]:= $Assumptions = t2 > t1 > > > Out[30]= t2 > t1 > > > In[31]:= TrueQ[(t2 - t1) > 0] > > > Out[31]= False > > ------------------------------------------------------ > > > I would expect TrueQ to return True, not False. Why does it return Fals= e? > > > And how can I test whether t2-t1 is positive? > > > Thanks.