I find some things to be a bit difficult to understand in math. As such, I will put some “jargon” here. This is definitely not jargon, but a notation on how things are written.

  • In Norms and Spaces we defined a metric on a set as a function 𝑑:𝑆×𝑆 but what does that even mean? 𝑆×𝑆 is the Cartesian product, or the set of all ordered pairs (𝑥,𝑦) where x and y both come from S. Ex. if 𝑆={1,2} then 𝑆×𝑆={(1,1),(1,2),(2,1),(2,2)}. Furthermore, 𝑑:𝑆×𝑆 means that 𝑑 is a function whose input is one such pair (𝑥,𝑦) and whose output is a real number. So 𝑑(𝑥,𝑦) is a single real number for each pair.
  • The notation is used when we are defining something new, while = implies regular equality.