What does the sign $\propto$ mean? I am a computer scientist, and one of my professors today used the symbol $\propto$. I tried to search that using google, but it returns no results, and I do not even know its name.
So, I would like to ask, what does the operator $\propto$ mean? What is its name, and how is it used?
 A: Since you say you're a computer scientist, it should be mentioned that Garey & Johnson use $A \propto B$ in their book Computers and Intractability – A guide to the Theory of NP-Completeness [1, page 34] to mean that there is a polynomial transformation from $A$ to $B$.
[1] Michael R Garey and David S Johnson. Computers and intractability, volume 174. Freeman
New York, 1979.
A: $A\propto B$ means that $A$ is directly proportional to $B$. This means that there exists some constant $k$ such that $A=kB$.
A: Besides direct proportionality, you might also see something like
$$ \frac{4n^2+1}{n}\propto n \text{ as }n\to\infty$$
which might rigorously be defined as:
$$ \exists C \forall \varepsilon>0 \exists N\forall n>N: \left|\frac{4n^2+1}{n}-Cn\right|<\varepsilon $$
meaning there exists a constant $C$ such that for large $n$, $\frac{4n^2+1}{n}$ is approximately equal to $Cn$ (and in this case $C=4$).
edit:
The definition I gave above is very strong, you might weaken it to
$$ \exists c_1,c_2\exists N\forall n>N: c_1n<\frac{4n^2+1}{n}<c_2n $$
in which case we would also have $\frac{4n^2+1}{n}+\sin(n)\propto n$ (which would make sense because the sine becomes less important as $n$ grows).
