Summation is one of the simplest mathematical operations at which there is a mutual addition of all summable (put) sizes. In spite of the fact that this mathematical operation is quite simple, it is worth understanding in more detail what is the sum.
The word "sum" came from Latin. The Latin word summa designated "a result, result". In its modern value the word began to be consumed at the end of the 15th century. The sum - an addition synonym. At addition a certain set of various sizes which will be put subsequently undertakes and the new size which will be result of this summation will be received. Sizes which underwent summation are called composed. The sum including several composed has a number of properties: - a + b = b + a (from change of the places composed the sum does not change); - a + (b + c) = (a + b) + c (from sequence of addition composed the sum does not change); - (and + b) * with = a*s + b*c (the general multiplier behind brackets has to be increased by everything composed in these brackets); - with * (and + b) = c*a + c*b (from change of the place of the general multiplier the sum does not change). The sum can be presented in the simplest form as the result of summation of A received at addition of various sizes a1, a2, a3, etc.: A = a1+a2+a3... But in mathematics the special sign which designates the sum is applied to bigger convenience of record. It is the sign? (sigma). Like simple brackets, behind the sign "sigma" it is possible to expose a certain quantity composed which need to be put. It will look so: A =? an where an is composed, n is a total number of the data composed. As opposed to summation there is a subtraction operation. At subtraction a certain other size is subtracted from a certain size therefore the first decreases by value of the second. If deductible size is more than that from which it is subtracted, then the result can be negative. It is also possible to understand as subtraction and addition of negative and positive numbers, for example: (-7) + 10 = 310 - 7 = 3 The actions Described above are possible thanks to one of properties of addition: from change of the places composed the sum does not change.