# Length of nested tuples

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:
• $$\lvert S_1 \rvert = 2$$
• $$\lvert S_2 \rvert = 4$$
• $$\lvert S_3 \rvert = 5$$
• Yes, and yes, what you wrote makes sense. Jan 27 at 7:12

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 $$n=\dim(V)$$