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 $I$ is the indexing set