Difference between revisions of "Addition"

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'''Addition''' is the name given to the [[mathematical]] [[function]] which involves the combination of two values, resulting in a directly related linear increase. The sum ''a + b'' can be interpreted as a [[binary]] operation that combines ''a'' and ''b'', in an algebraic sense, or it can be interpreted as the addition of ''c'' more units to ''b''. Under the latter interpretation, the parts of a sum ''c + a'' play [[symmetric]] roles, and the operation ''a + c'' is viewed as applying the [[unary]] operation ''+b'' to ''a''. Instead of calling both ''a'' and ''b'' [[addend]]s, it is more appropriate to call a the augend in this case, since a plays a passive role. The unary view is also useful when discussing [[subtraction]], because each unary addition operation has an [[inverse operations|inverse]] unary subtraction operation and vice versa.
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'''Addition''' is the mathematical operation that combines two or more numbers to produce their [[sum]].
  
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[[category:mathematics]]
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For simple addition of [[whole number]]s, it is easy to add by counting steps. If we consider 6 + 4, then we can start at 6, then add 1 four times: 7, 8, 9, 10. Thus, 6 + 4 is 10.
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For more complex addition, [[long addition]] can be carried out.
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Addition is [[commutative]], thus a + b = b + a.
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==Formal definition==
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It is helpful to see addition in terms of [[function]]s - addition adds one number (a) to another number (b) to make their sum (c).
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Thus,
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a + b = c.
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Its reverse function, or [[inverse operation]], is [[subtraction]], which moves the other way:
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c - b = a.
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It is possible to add a negative number, but this is the same as subtracting that number:
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a + (-b) = a - b.
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[[Category:Arithmetic]]

Latest revision as of 01:00, July 13, 2016

Addition is the mathematical operation that combines two or more numbers to produce their sum.

For simple addition of whole numbers, it is easy to add by counting steps. If we consider 6 + 4, then we can start at 6, then add 1 four times: 7, 8, 9, 10. Thus, 6 + 4 is 10.

For more complex addition, long addition can be carried out.

Addition is commutative, thus a + b = b + a.

Formal definition

It is helpful to see addition in terms of functions - addition adds one number (a) to another number (b) to make their sum (c).

Thus,

a + b = c.

Its reverse function, or inverse operation, is subtraction, which moves the other way:

c - b = a.

It is possible to add a negative number, but this is the same as subtracting that number:

a + (-b) = a - b.

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