Addition is a mathematical operation that represents combining collections of objects together into a larger collection. It is signified by the plus sign (+). For example, in the picture on the right, there are 3 + 2 apples—meaning three apples and two other apples—which is the same as five apples. Therefore, 3 + 2 = 5. Besides counting fruits, addition can also represent combining other physical and abstract quantities using different kinds of numbers: negative numbers, fractions, irrational numbers, vectors, decimals and more.
Addition follows several important patterns. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication. All of these rules can be proven, starting with the addition of natural numbers and generalizing up through the real numbers and beyond. General binary operations that continue these patterns are studied in abstract algebra.
Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months and even some animals. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.
Famous quotes containing the word addition:
“The addition of a helpless, needy infant to a couples life limits freedom of movement, changes role expectancies, places physical demands on parents, and restricts spontaneity.”
—Jerrold Lee Shapiro (20th century)
“As easy mayst thou fall
A drop of water in the breaking gulf,
And take unmingled thence that drop again,
Without addition or diminishing,
As take from me thyself and not me too.”
—William Shakespeare (15641616)
“Napoleon wanted to turn Paris into Rome under the Caesars, only with louder music and more marble. And it was done. His architects gave him the Arc de Triomphe and the Madeleine. His nephew Napoleon III wanted to turn Paris into Rome with Versailles piled on top, and it was done. His architects gave him the Paris Opera, an addition to the Louvre, and miles of new boulevards.”
—Tom Wolfe (b. 1931)