Length of nested tuples

Question

Assume we have the following tuple of tuples: S = ((1,2), (2,3,4,5), (4,5,6,7,8)).

• There are three nested tuples. To write the length of S (the number of nested tuples), is it correct notation to write $\lvert S \rvert = 3$?
• How do one then write the notation for the length of a nested tuple? $\lvert S_i \rvert, i=1,2,..,\lvert S \rvert$? Examples:
  • $\lvert S_1 \rvert = 2$
  • $\lvert S_2 \rvert = 4$
  • $\lvert S_3 \rvert = 5$

Answer 1

This notation is not frequently used to denote the length of a tuple. Now it depends where you want to define "length of a tuple". In linear algebra, analysis,$\cdots$ we usually define a natural number $n\in\mathbb{N}$ to denote dimension of Euclidean space $\mathbb{R}^{n}$ or for a vector space $V$ we sometimes use $n=\dim(V)$