Sometimes, order matters.
We can write $(a, b)$ as an ordered pair.

  • $a$ is the first element and $b$ is the second
  • $(a, b) = (c, d)$ if and only if $a = c$ and $b = d$
  • if $a \neq b$ then $(a, b) \neq (c, d)$
    • $(1, 2) \neq (2, 1)$
  • This extends to ordered triple, quadruples, etcetc
  • These may also be called vectors/sequences :p