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Addition is commutative, meaning that one can change the order of the terms in a sum, but still get the same result. Symbolically, if a and b are any two numbers, then a + b = b + a. The fact that addition is commutative is known as the "commutative law of addition" or "commutative property of addition".
For example, (2 + 3) × 4 = 20 forces addition to precede multiplication, while (3 + 5) 2 = 64 forces addition to precede exponentiation. If multiple pairs of parentheses are required in a mathematical expression (such as in the case of nested parentheses), the parentheses may be replaced by other types of brackets to avoid confusion, as in [2 ...
Arithmetic is closely related to number theory and some authors use the terms as synonyms. [8] However, in a more specific sense, number theory is restricted to the study of integers and focuses on their properties and relationships such as divisibility, factorization, and primality. [9] Traditionally, it is known as higher arithmetic. [10]
Addition is the mathematical process of putting things together. Addition may also refer to: Addition (logic), a simple logic argument form; Addition reaction, a chemical reaction combining molecules "Addition", a song by No Devotion from Permanence; A room or wing added onto a building after initial construction through renovation
An addendum or appendix, in general, is an addition required to be made to a document by its author subsequent to its printing or publication. It comes from the gerundive addendum , plural addenda , "that which is to be added", from addere [ 1 ] ( lit.
The definition of addition α + β can also be given by transfinite recursion on β. When the right addend β = 0, ordinary addition gives α + 0 = α for any α. For β > 0, the value of α + β is the smallest ordinal strictly greater than the sum of α and δ for all δ < β. Writing the successor and limit ordinals cases separately: α + 0 = α
Example of addition with carry. The black numbers are the addends, the green number is the carry, and the blue number is the sum. In the rightmost digit, the addition of 9 and 7 is 16, carrying 1 into the next pair of the digit to the left, making its addition 1 + 5 + 2 = 8. Therefore, 59 + 27 = 86.
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