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Subtraction is itself a sort of inverse to addition, in that adding x and subtracting x are inverse functions. Given a set with an addition operation, one cannot always define a corresponding subtraction operation on that set; the set of natural numbers is a simple example.
Subtraction is the inverse of addition. In it, one number, known as the subtrahend, is taken away from another, known as the minuend. The result of this operation is called the difference. The symbol of subtraction is . [47] Examples are = and =. Subtraction is often treated as a special case of addition: instead of subtracting a positive ...
A subtraction problem such as is solved by borrowing a 10 from the tens place to add to the ones place in order to facilitate the subtraction. Subtracting 9 from 6 involves borrowing a 10 from the tens place, making the problem into +. This is indicated by crossing out the 8, writing a 7 above it, and writing a 1 above the 6.
Conversely to floating-point arithmetic, in a logarithmic number system multiplication, division and exponentiation are simple to implement, but addition and subtraction are complex. The level-index arithmetic (LI and SLI) of Charles Clenshaw, Frank Olver and Peter Turner is a scheme based on a generalized logarithm representation.
Subtraction also obeys predictable rules concerning related operations, such as addition and multiplication. All of these rules can be proven, starting with the subtraction of integers and generalizing up through the real numbers and beyond. General binary operations that follow these patterns are studied in abstract algebra.
In particular, multiplying or adding two integers may result in a value that is unexpectedly small, and subtracting from a small integer may cause a wrap to a large positive value (for example, 8-bit integer addition 255 + 2 results in 1, which is 257 mod 2 8, and similarly subtraction 0 − 1 results in 255, a two's complement representation ...
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