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In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
A common construction of the set of real numbers is the Dedekind completion of the set of rational numbers. A real number is defined to be a Dedekind cut of rationals: a non-empty set of rationals that is closed downward and has no greatest element. The sum of real numbers a and b is defined element by element:
The concept of a decimal digit sum is closely related to, but not the same as, the digital root, which is the result of repeatedly applying the digit sum operation until the remaining value is only a single digit. The decimal digital root of any non-zero integer will be a number in the range 1 to 9, whereas the digit sum can take any value.
In addition, + represents the operation of addition, which results in a sum, while − represents subtraction, resulting in a difference. [1] Their use has been extended to many other meanings, more or less analogous. Plus and minus are Latin terms meaning "more" and "less", respectively.
For the number of representations of a positive integer as a sum of squares of k integers, see Sum of squares function. Fermat's theorem on sums of two squares says which primes are sums of two squares. The sum of two squares theorem generalizes Fermat's theorem to specify which composite numbers are the sums of two squares. Pythagorean triples ...
An abundant number whose abundance is greater than any lower number is called a highly abundant number, and one whose relative abundance (i.e. s(n)/n ) is greater than any lower number is called a superabundant number; Every integer greater than 20161 can be written as the sum of two abundant numbers. The largest even number that is not the sum ...
The same carry bit is also generally used to indicate borrows in subtraction, though the bit's meaning is inverted due to the effects of two's complement arithmetic. Normally, a carry bit value of "1" signifies that an addition overflowed the ALU , and must be accounted for when adding data words of lengths greater than that of the CPU.
Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of ...