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  2. Addition - Wikipedia

    en.wikipedia.org/wiki/Addition

    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".

  3. Proofs involving the addition of natural numbers - Wikipedia

    en.wikipedia.org/wiki/Proofs_involving_the...

    Basic arithmetic properties (zoom in for induction proofs) This article contains mathematical proofs for some properties of addition of the natural numbers: the additive identity, commutativity, and associativity. These proofs are used in the article Addition of natural numbers.

  4. Associative property - Wikipedia

    en.wikipedia.org/wiki/Associative_property

    In mathematics, addition and multiplication of real numbers are associative. By contrast, in computer science, addition and multiplication of floating point numbers are not associative, as different rounding errors may be introduced when dissimilar-sized values are joined in a different order. [7]

  5. Commutative property - Wikipedia

    en.wikipedia.org/wiki/Commutative_property

    The Egyptians used the commutative property of multiplication to simplify computing products. [7] [8] Euclid is known to have assumed the commutative property of multiplication in his book Elements. [9] Formal uses of the commutative property arose in the late 18th and early 19th centuries, when mathematicians began to work on a theory of ...

  6. Order of operations - Wikipedia

    en.wikipedia.org/wiki/Order_of_operations

    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 ...

  7. Distributive property - Wikipedia

    en.wikipedia.org/wiki/Distributive_property

    In mathematics, the distributive property of binary operations is a generalization of the distributive law, ... addition distributes over the maximum operation, ...

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