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In mathematics, an empty product, or nullary product or vacuous product, is the result of multiplying no factors.It is by convention equal to the multiplicative identity (assuming there is an identity for the multiplication operation in question), just as the empty sum—the result of adding no numbers—is by convention zero, or the additive identity.
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.
It becomes easier to solve with less calculations required. A reasonable value for u could be u = t·t/4 for the corresponding t based on the largest product of two factors whose sum are t being (t/2)·(t/2). Now the problem has a unique solution in the ranges 47 < t < 60, 71 < t < 80, 107 < t < 128, and 131 < t < 144 and no solution below that ...
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 b more units to a. Under the latter interpretation, the parts of a sum a + b play asymmetric roles, and the operation a + b is viewed as applying the unary operation +b to a. [20]
A simple example is the set of non-zero rational numbers. Here identity 1 is had, as opposed to groups under addition where the identity is typically 0. Note that with the rationals, zero must be excluded because, under multiplication, it does not have an inverse: there is no rational number that can be multiplied by zero to result in 1.
In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors.For example, 21 is the product of 3 and 7 (the result of multiplication), and (+) is the product of and (+) (indicating that the two factors should be multiplied together).
A census taker approaches a woman leaning on her gate, number 14, and asks about her children. She says, "I have three children and the product of their ages is seventy–two. The sum of their ages is the number on this gate." The census taker does some calculation and claims not to have enough information.
Starting from the rightmost digit, each pair of digits is added together. The rightmost digit of the sum is written below them. If the sum is a two-digit number then the leftmost digit, called the "carry", is added to the next pair of digits to the left. This process is repeated until all digits have been added. [65]