An empty sum is a sum with zero terms and is equal to 0 (the additive identity). We can see this algebraically using repeated addition. For example, adding up 5 three times is equal to 5 + 5 + 5 = 5 · 3 = 15. Following this same reasoning, adding up 5 zero times is equal to 5 · 0 = 0. An empty product is a product with zero terms. Apply a similar process as above to show that an empty product is equal to 1 (the multiplicative identity).