Steven Senger: Math notation

I tend to use the same notation pretty consistently, but it might not be standard for everyone. Here is a list of some things I use commonly. $\dpi{100} $If $E$ is some set, I often use $|E|$ to mean the size of the set. If $A$ is a subset of some ring, I typically denote its sum set by $A+A=\{a+b:a,b\in A \}$, and its product set by $AA=\{ab:a,b\in A \}$.$ $\dpi{100} $If $X(n)$ and $Y(n)$ are two functions that change as some parameter $n$ grows large, then we write $X(n)\lesssim Y(n)$ if there exist some positive constants, $C$ and $N$, independent of $n$, such that for all $n\geq N$, $X(n)\leq CY(n).$ If $X(n)\lesssim Y(n)$ and $Y(n)\lesssim X(n)$, we write $X(n)\approx Y(n)$. To also bury logarithmic factors, we write $X(n)\lessapprox Y(n)$ when for every $\epsilon>0$, there exist some positive constants, $C_\epsilon$ and $N_\epsilon$, independent of $n$, such that for all $n\geq N_\epsilon, X(n)\leq C_\epsilon Y(n).$$

Steven Senger

Monday, July 30, 2012

Math notation

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