The set of numbers determined by short circuit of a set of natural numbers concerning such arithmetic operations as addition and subtraction is called whole. Thus, whole are number 0, 1, 2, etc. and also-1,-2, etc.
Instruction
1. Negative numbers were for the first time used in mathematics by such persons as Michael Stifel (book "Full Arithmetics" of 1544) and Nicolas Chuc.
2. Mark out the following main algebraic properties of integers: – isolation; – associativity; – commutativity; – existence of a neutral element; – existence of an opposite element; – distrubutivnost.
3. The isolation concerning operation of addition means that the sum of two integers will give an integer. Similarly, the work of two integers will also be whole.
4. The property of associativity concerning addition tells that a + (b + c) = (a + b) + with. The same way it is expressed also concerning multiplication: a × (b × c) = (a × b) × with.
5. The property of commutativity means that a + b = b + a. In other words, from shift of the places composed the sum does not change. For multiplication: × b = b × a. From shift of places of multipliers the work does not change.
6. At addition operation a neutral element is zero: a + 0 = a. At multiplication – unit: a × 1 = a. Also for an integer there is its opposite element: a + (−a) = 0.
7. The property of distributivity consists in the following: a × (b + c) = (a × b) + (× c). In other words, the work of an integer and the sum of other integers is equal to the sum of the work of this number every composed.
8. Positive the integer is called when it more than zero. If it less than zero, it is called as negative. Zero does not belong neither to positive numbers, nor to negative. The following properties are fair concerning integers: – if a
In programming languages there is a type of data which is called "integer". In many of them it is one of the main. However this type of data actually not absolutely corresponds to a class of integers. It is only a subset. It is connected with the fact that – infinitely there is a lot of integers, and memory of the computer is limited whatever big it was.
9. In programming languages there is a type of data which is called "integer". In many of them it is one of the main. However this type of data actually not absolutely corresponds to a class of integers. It is only a subset. It is connected with the fact that – infinitely there is a lot of integers, and memory of the computer is limited whatever big it was.