The third video on near-number arithmetic is now online, discussing ☆-forms for both arithmetic and powers, including the way in which they all stem from the most basic one: +∞ + –∞.  Key learning goals are:

• to review the meaning of the near-number ☆ and what we mean by a "☆-form" as a dead-end in a computation,
• to derive all basic ☆-forms for arithmetic and powers, noting the way in which they're all connected,
• and to clear up misconceptions about "indeterminacy" and why "∞ – ∞" not being zero doesn't run at all against the fact that for any real number a, we do have a – a = 0.