Author 
Comment/Response 
yehuda

06/06/13 09:50am
I do not see an error here.
You have fallen into the trap of numerical accuracy near critical points...
The denominator of T[z] approaches 0 for z>1/3 so the whole expression is ComplexInfinity
So what would you expect?
With
T[x]S[x] you first tray to calculate each function (numerically) and then take the difference
Try
Simplify[T[x]S[x]]
you will get an identical zero
try also T[1/4]S[1/4]
again zero
trying T[0.333] etc. is calculating T[x] for a point which is near the root but with a fixed accuracy
if you calculate T[0.3333333333333333] you will get a (much) higher value since it is closer to the root
try increasing the precision (say 100 digits )
T[0.333333`100]  S[0.333333`100]
you will get a number which is quite close to zero
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