The meaning of $\Bbb R^\Bbb N$

Question

I know that $\Bbb R$ is the real line, that $\Bbb R^{\Bbb 2}$is some pair of numbers of numbers from the real line and that $\Bbb R^3$ is a triplet of numbers from the real line etc.. So I assume that $\Bbb R^\Bbb N $is an infinite selection of numbers from the real line , is that correct ? if so what specifically does it mean to say $B=\{a \in \Bbb R ^\Bbb N |\exists C \in \Bbb R \forall n \in \Bbb N :|a(n)|<C\}$ ?

Answer 1

Precisely speaking, $\mathbb{R}^\mathbb{N}$ is the set of real sequence. It is not even an infinite selection of real numbers, but a COUNTABLE selection of real numbers.