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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. 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 ...

  4. Proofs involving the addition of natural numbers - Wikipedia

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

    The base case b = 0 follows immediately from the identity element property (0 is an additive identity), which has been proved above: a + 0 = a = 0 + a. Next we will prove the base case b = 1, that 1 commutes with everything, i.e. for all natural numbers a, we have a + 1 = 1 + a.

  5. 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]

  6. Order of operations - Wikipedia

    en.wikipedia.org/wiki/Order_of_operations

    If each subtraction is replaced with addition of the opposite (additive inverse), then the associative and commutative laws of addition allow terms to be added in any order. The radical symbol √ is traditionally extended by a bar (called vinculum) over the radicand (this avoids the need for parentheses around the radicand). Other functions ...

  7. Elementary arithmetic - Wikipedia

    en.wikipedia.org/wiki/Elementary_arithmetic

    The addition of two numbers is expressed with the plus sign (+). [6] It is performed according to these rules: The order in which the addends are added does not affect the sum. This is known as the commutative property of addition. (a + b) and (b + a) produce the same output. [7] [8]

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