In arithmetic, the remainder (or residue) is the amount "left over" after the division of two integers which cannot be expressed with an integer quotient.

The general form of a linear equation can be expressed as a = q × d + r. In this equation, q can be referred to as the quotient and d as the divisor, while r as the remainder. The equation can be transformed to find the remainder as: r = a - q × d. However, a and d must be natural numbers, with d being non-zero. The quotient is the integer result (rounded down) of the division of a by d. The remainder must also be an integer.

If a and d are natural numbers, with d non-zero, it can be proven that there exist unique integers q and r, such that a = qd + r and 0 ≤ r < d. The number q is called the quotient, while r is called the remainder. The division algorithm provides a proof of this result and also an algorithm describing how to calculate the remainder.

If a and d are integers, with d non-zero, then a remainder is an integer r such that a = qd + r for some integer q, and with |r| < |d|.

Steven John Wilson (born 3 November 1967) is an English musician, best known as the founder, lead guitarist, singer and songwriter of progressive rock band Porcupine Tree. He is involved in many other bands and musical projects both as musician and producer (including No-Man and Blackfield) and also maintains a solo career.

Wilson is a self-taught producer, audio engineer, guitar and keyboard player, playing other instruments as and where required (including bass guitar, concert harp, hammered dulcimer and flute).

He used to split his living time between Tel Aviv and London, England, but he no longer holds a permanent residence in Tel Aviv.

Born in Kingston upon Thames, London, England (but brought up in Hemel Hempstead, Hertfordshire, England from the age of 6)^{[citation needed]}, Wilson discovered his love for music around the age of 8. It began one Christmas when his parents bought presents for each other in the form of LPs. His father and mother received Pink Floyd's The Dark Side of the Moon and Donna Summer's Love to Love You Baby, respectively. The young Steven spent much of his childhood listening to these albums in "heavy rotation", as he once commented.