Integers arise to make total the operation of subtraction as the inverse of the primary arithmetical operation of addition. As such, it serves

• To provide temperature measurement scales, in which it is useful and even meaningful to distinguish "above and below zero". (The zero of the celsius temperature scale is the triple point at which H₂O can exists as ice, water, and gas.)
• To provide topographic measurement scales, in which it is useful and meaningful to distinguish "above and below sea level".
• To provide an economic scale for debit-credit bookkeeping, for evaluating stocks, bonds, and other securities and other fiduciary concerns.

Etc.

Ancient Hindus are said to have developed an analogous scales using red to denote "positive nymbers" and blue to denote "negative numbers". (Perhaps this labeling arose from the tinging of human skin in very hot or very cold climate.