∞−∞ is undefined · ℵ₀ ℵ₁ and ω are different objects · treating ∞ as a number leads to 1=0 · runs locally
infinity is a family of objects: cardinal ℵ₀ (countable), ℵ₁ (uncountable), ordinal ω, projective ∞, extended reals ±∞ · each has different rules · ℕ and ℚ have the same cardinality · ℝ is strictly larger