| Subtraction |
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| CATEGORIES ABOUT SUBTRACTION | |
| elementary arithmetic | |
| binary operations | |
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Subtraction is one of the four basic Arithmetic operations; it is essentially the opposite of Addition . Subtraction is denoted by an Minus Sign in Infix Notation . The traditional names for the parts of the Formula c are ''minuend'' (''c'') − ''subtrahend'' (''b'') = ''difference'' (''a''). The words "minuend" and "subtrahend" are virtually absent from modern usage; Linderholm charges "This terminology is of no use whatsoever." However, "difference" is very common. Subtraction is used to model several closely related processes: #From a given collection, take away (subtract) a given number of objects. #Combine a given measurement with an opposite measurement, such as a movement right followed by a movement left, or a deposit and a withdrawal. #Compare two objects to find their difference. For example, the difference between $800 and $600 is $800 − $600 = $200. In or Commutative — in fact, it is Anticommutative — but addition of signed numbers is both. BASIC SUBTRACTION: INTEGERS Imagine a Line Segment of Length ''b'' with the left end labeled ''a'' and the right end labeled ''c''. Starting from ''a'', it takes ''b'' steps to the right to reach ''c''. This movement to the right is modeled mathematically by Addition : a From ''c'', it takes ''b'' steps to the ''left'' to get back to ''a''. This movement to the left is modeled by subtraction: c Now, imagine a line segment labelled with the numbers 1 , 2 , and 3 . From position 3, it takes no steps to the left to stay at 3, so 3 − 0 = 3. It takes 2 steps to the left to get to position 1, so 3 − 2 = 1. This picture is inadequate to describe what would happen after going 3 steps to the left of position 3. To represent such an operation, the line must be extended. To subtract arbitrary Natural Number s, one begins with a line containing every natural number (0, 1, 2, 3, 4, ...). From 3, it takes 3 steps to the left to get to 0, so 3 − 3 = 0. But 3 − 4 is still invalid since it again leaves the line. The natural numbers are not a useful context for subtraction. The solution is to consider the Integer number line (…, −3, −2, −1, 0, 1, 2, 3, …). From 3, it takes 4 steps to the left to get to −1, so :3 − 4 = −1. SEE ALSO ;Algorithms NOTES AND REFERENCES |
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