# Tuple

## Definition

A tuple is a (potentially) mixed type vector of things. However as it may not be in a vector space we do not call it a vector.

## Examples

$(1,2,3,\{a\})$ is the tuple of the numbers 1, 2 and 3 and the set $\{a\}$

## Short hands

• Countably infinite tuples
• $(a_n)_{n=1}^\infty$
• $(a_1,...)$ (using numbers implies countable)
• Finite tuples
• $(a_1,...,a_n)$
• $(a_i)_{i=1}^n$
• Indexed tuples
• $(a_\alpha)_{\alpha\in I}$ where [ilmath]I[/ilmath] is the indexing set