👉 In mathematics, an ideal is a subset of a ring that contains all multiples of another element. For example, in the ring of integers modulo 5, there are five multiples of any integer (±1, ±2, ±3, ±4, and ±5) because each multiple of one number can be multiplied by any other number to get a new multiple. An ideal is defined as a subset that contains all multiples of another element. In the context of mathematics, an ideal is often