It seems obvious that 2 + 2 ≠ 5…

  • “∈” means “element of” “belongs to” or “in”.
  • “ℕ” is a symbol for the natural numbers (0, 1, 2, 3 … etc.).
  • “¬” means “not”.
  • “⇔” means “if and only if”.
  1. For every natural number x, the number after x is also a natural number.
  2. For any two natural numbers x and y, if x = y, then S(x) = S(y) and if S(x) = S(y) then x = y
  3. 0 does not come after any natural number.
  4. Any natural number plus zero is itself
  5. For any two natural numbers x and y, x + S(y) = S(x + y)

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