Are these expressions correct logically?

Question

Which of the following expressions correct logically?

1. $\min (a,b)$ or $\min\{a,b\}$?
2. $a\times \Bbb R$ or $\{a\}\times \Bbb R$?

I saw these expressions (first one of each item) in many books but I think these are not correct logically. Am I right?

Answer 1

Both $\min(a,b)$ and $\min\{a,b\}$ are correct, since you can see $\min$ as a function of two variables:$$\min(x,y)=\begin{cases}x&\text{ if }x\leqslant y\\y&\text{ otherwise.}\end{cases}$$

Concerning the other question, yes, $a\times\mathbb R$ makes no sense (assuming that $a$ is a real number).