1/x → +∞ from right and −∞ from left · no consistent limit · division by zero breaks arithmetic · runs locally
division by zero: lim x→0⁺ 1/x = +∞ but lim x→0⁻ 1/x = −∞ · no single consistent value · algebra breaks: dividing by (a−b) when a=b is dividing by 0 · hidden division by zero allows any false claim