OK, I see. But when I saw
C=t/R*ln(V/(V-Vc))
I saw it as meaning "t over (all the rest of that stuff)", so no need for extra parens.
(That's the problem with text-based math ... we need tEx.)
Hi,
Parens are used to eliminate the ambiguity. For example, if i write:
K1=t/R*ln(V/(V-Vc))
and:
K2=t/R*ln(V/(V-Vc))
which one do i want to have everything after the 't' in the denominator, and which one do i want only the 'R' in the denominator?
What if one has it and one doesnt, how would we know which one has it and which one doesnt?
Following the rules of algebra, both of those only have 'R' in the denominator, so we really need parens to clear it up:
K1=t/R*ln(V/(V-Vc))
and:
K2=t/(R*ln(V/(V-Vc)))
Now we know that K1 only has 'R' while K2 has the whole part after the 't' in the denominator.
We really must use parens whenever there is a doubt or else the reader wont be able to evaluate it in the correct order. For example:
y=x^2*3/8*a/7+b/sqrt(2)/9/8/7/6/5/4/3/2
What is the true denominator there?
Another thing to watch out for is sometimes some authors still use the trig convention:
cos x
instead of the more proper:
cos(x)
Using "cos x" causes problems when we get something like:
cos x*2*pi
Is this "cos(x)*2*pi", or is it "cos(x*2)*pi", or is it "cos(x*2*pi)"? Anybodies guess
Note that if we write instead:
cos(x*2*pi)
there is no problem understanding how to evaluate this expression.
It gets even weirder than that though as with:
cos 2*pi*x+ph
which is meant to mean:
cos(2*pi*x+ph)
Note again the parens eliminate any doubt as to how to evaluate the expression.
The simple rule then is: "Use parens when there is any possibility of an alternate order of evaluation".