The distinction between < and <= is fairly meaningless when applied to a 
computed floating-point result.  I think the docs should be fixed to 
replace the < with <=.  In any case, the b <= N < a bit has the 
inequalities the wrong way around: presumably it was intended to read b < 
N <= a.  The docs for random.triangular should also be fixed in the same 
way.

(N.B. What *is* always true is that the result of random.random() is never 
1.0.  And that's a useful property---without it, random.uniform(a, b) can 
even return values *outside* the closed interval [a, b].)

To me, it doesn't seem worth slowing down random.uniform itself with extra 
checks: it's the sort of function that often gets called millions of times 
within a simulation, or numerical algorithm (e.g. Monte-Carlo 
integration), and it's trivial for the user to add his or her own check if 
necessary.

I also think it's a nice property that random.uniform currently degrades 
gracefully when a == b, producing the expected point distribution at a.  I 
wouldn't want to change that.

So:  +1 for amending the docs.  -1 for changing random.uniform.