Digits etc

  1. There are the symbols 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0. 1 is ⚫︎, 2 is ⚫︎⚫︎, etc., and 0 is nothing. When put together: For the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0, xy = x * (9 + 1) + y. For example: 23 = 2 * (9 + 1) + 3. 45 = 4 * (9 + 1) + 5. And 67 = 6 * (9 + 1) + 7.
  2. Importantly, the xy in that algebraic equation isn’t another way of writing x * y. In the present context, xy means writing the symbol for the number x in front of the symbol for the number y, with the possible numbers being from ⚫︎ to ⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎, e.g. writing the symbol 2 in front of the symbol 3.
  3. Put differently: For the digits (the term “digit” meaning a certain kind of symbol) 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0, the digit x written in front of the digit y = the number associated with the digit x * ⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎ + the number associated with the digit y.