0

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 $B=\{a \in \Bbb R ^\Bbb N |\exists C \in \Bbb R \forall n \in \Bbb N :|a(n)|<C\}$ ?

excalibirr
  • 2,795
  • 1
    It is the collection of functions $\mathbb{N} \to \mathbb{R}$, that is, the real sequences. In general, $A^B$ is the collection of functions $B \to A$. Think of $B$ as the index set. – copper.hat Jul 31 '18 at 05:16
  • No, $\mathbb R$ is not "some pair of numbers", it is the set of all pairs of real numbers. $(\sqrt2,\pi)$ is some pair of real numbers, but $(\sqrt2,\pi)\ne\mathbb R.$ – bof Jul 31 '18 at 05:31

1 Answers1

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.

Loafy Loafer
  • 937
  • 8
  • 25