# What is the difference between xx and *?

Nov 29, 2016

When writing by hand, it is common to use $\cdot$ or parentheses (e.g. $\left(2 x\right) \left(4 y\right) = 8 x y$) to denote multiplication rather than $\times$ as it is easy to confuse $\times$ with $x$ without very precise handwriting. As one progresses in mathematics, it is standard to see $\times$ used less and less in comparison to $\cdot$ or omitting a symbol altogether for denoting multiplication.
In more advanced courses, the meanings of $\cdot$ and $\times$ may differ depending on the context. For example, in vector calculus, $\cdot$ denotes a dot product and $\times$ denotes a cross product. In abstract algebra, $\times$ may be used to denote a direct product. For example, $\mathbb{R} \times \mathbb{R}$ is the set of all ordered pairs $\left(x , y\right)$ where $x$ and $y$ are in $\mathbb{R}$ (the set of real numbers).