negative number

(mathematics) A real number that is less than 0.

In contrast to the positive number, typically referred to without qualification, the negative number is a notional entity. Written characteristically with a dash or ‘minus sign’ preceding the digit(s), a negative number conceptually represents the amount that would have to be added before there would be nothing, i.e. zero. The amount needing to be added is the said number without the preceding minus sign. In mathematics that positive amount would be termed the arithmetic value or absolute value of the original number, identically the value of the corresponding positive number; the term algebraic value pertains to the distinct negative/positive signed value of any number.

For integers, the expression of negative numbers is simple and unambiguous. The same might be said of fractions, etc., but the traditional practice with logarithms presents a contrary picture; there the negative sign applies only to the integer part, the fractional being always positive. Thus what would normally be written -1.234 5 is, being identically -2 + 0.765 5, written for logarithms as -2.765 5 (or, to be distinctive, with the minus sign above the integer). The reason for this peculiarity can be seen by attempting to add, without machine assistance, a mixture of negative and positive numbers of several digits each; the usual resolution is to add the positives, then add the negatives and subtract their total. Logarithms are necessarily of several digits in the fractional part, but rarely of more than one digit in the integer part. The dichotomous practice with the sign allows straight addition of the fractional, constrains the awkwardness of mixed addition and subtraction to a simpler domain, and simplifies the task of looking up logarithms and their functional reciprocals (antilogarithms) in tables.

In financial statements, enclosure by curved brackets is typically used for negative values, rather than a preceding minus sign. The labels DB for debit and CR for credit are used more often in basic accounting to express opposite signs, the pertinent mathematical signs depending on context.