**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.

Read more about Addition: Notation and Terminology, Interpretations, Addition of Natural and Real Numbers, Generalizations, In Literature

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### Famous quotes containing the word addition:

“But the best read naturalist who lends an entire and devout attention to truth, will see that there remains much to learn of his relation to the world, and that it is not to be learned by any *addition* or subtraction or other comparison of known quantities, but is arrived at by untaught sallies of the spirit, by a continual self-recovery, and by entire humility.”

—Ralph Waldo Emerson (1803–1882)

“Depend upon it there comes a time when for every *addition* of knowledge you forget something that you knew before. It is of the highest importance, therefore, not to have useless facts elbowing out the useful ones.”

—Sir Arthur Conan Doyle (1859–1930)

“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)