
CSC 103 Lecture Notes Week 1 - ghosh
http://users.csc.calpoly.edu/~gfisher/classes/103/lectures/week1.html
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pjakma
I think the table in IX is wrong about log^2(x) being the same as log(log(x)).
For me, and my impression is for many others, log^2(x) means log(x)log(x).

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gms7777
I agree that log^2(x) is more commonly used to refer to log(x)log(x) than
log(log(x)), though I've seen it both ways (I think its somewhat dependent on
the conventions of the field). That said, the notation is both ambiguous and
non-sensical (you're not squaring the operator...), and at least in my
opinion, should be avoided in favor of the less ambiguous (log(x))^k

Gauss actually had some choice words about the notationally similar sin^2(x):
"Sin2 φ is odious to me, even though Laplace made use of it; should it be
feared that sin2 φ might become ambiguous, which would perhaps never occur, or
at most very rarely when speaking of sin(φ2), well then, let us write (sin
φ)2, but not sin2 φ, which by analogy should signify sin (sin φ)"

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aweyl
Using log^2(x) to denote log(log(x)) is far from nonsensical. It makes sense
when keeping in mind the fact that function composition is an operation on
functions much like addition and multiplication. For example, we can write
f(f(x)) = (f∘f)(x) = f^2(x) f(f(f(x))) = (f∘(f∘f))(x) = (f∘f∘f)(x) an so on.
We can see that when composing a function with itself many times it is much
easier to write f^n(x) than the alternative.

Using log^2(x) to mean (log(x))^2 is a shortcut that typesetters took in order
to save time and is not as widely used in mathematics.

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gms7777
I agree with you. I only meant to refer to the (log(x))^2 case as nonsensical,
though I think my wording was ambiguous. I understand its a hort-cut but it
doesn't make mathematical sense as a notation. I think it makes more in the
log(log(x)) case, for the same reasons you've pointed out. Though, at least in
my experience in my field (theoretical CS), I see it used as (log(x))^2 far
more often than log(log(x)).

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pjakma
Yes, log^2(x) seems almost always to be used to mean [log(x)]^2 in the routing
theory papers I tend to read.

I agree with you though that using log^2(x) for [log(x)]^2 is horridly
ambiguous notation that should be avoided! (Which reminds me, I should go and
check my thesis for this ;) ).

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kinofcain
I was at poly when they switched the CSC program from c++ to java, had been
secretly hoping they switched back. Oh well :-) good to see poly getting some
HN love.

