1. The remaining integer when a division of an integer by another is performed; if l = m / p + r, where l, m, p, and r are integers and r is less than p, then r is the remainder when l is divided by p.

2. The remaining polynomial when division of a polynomial is performed; if l = m / p + r, where l, m, p, and r are polynomials, and the degree of r is less than that of p, then r is the remainder when l is divided by p.

3. The remaining part of a convergent infinite series after a computation, for some n, of the first n terms.