The numerical sets are sets that contain a defined range of numbers. Have the effect of all possible combinations of digits of the numbers of the alphabet. The alphabet of the numbers is the set that contains all the digits, such as Alfa = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} . Taking
n items from A, also repeated, if we have them in sequence, we have created a number which, in turn, according to certain rules of arithmetic represents a quantity of objects.
Here are some sequences of numbers: 124, 895, 21, 7, 993, 567, 33188. Each sequence is just a number and represents a quantity, also should be noted that not represent a number using a mathematical set as the second set theory, a set can not contain repetitive elements and the order in which they are arranged is immaterial. (Eg: the set A = {9, 9, 3} does not make sense, since the element 9 is repeated and the order can be changed, and it is always the same set, then B = {3, 9 } is equal to A.
List all items in a set number, it is not convenient since the main numerical sets have infinite elements.
To determine a set number, as all the existing collections, we must first determine its entirety or by listing or by characteristic properties.
If we use numbers to express how much we have to create rules that allow to determine these quantities. For example, the element 0 of the whole Alfa nothing expresses a quantity, that is nothing ("I have 0 apples 'equals' I do not have apples), while the first element expresses a quantity equivalent to a single object, and so on ... however we all know the amount that each icon corresponds to single digit. If we need to count more than 9 items, we can not use a single digit, so there are rules that allow the expression of infinite quantities.
repeat, the numbers are sequences of digits, each digit is contained in a box and the amount that represents the amount depends on the location of the box in the sequence. Going from right to left, each next box is a larger amount multiplied by 10 (cardinality of Alfa), and this is a fundamental rule that provides us with a numbering system to represent quantities. Thus, we can say that the first box represents the unity, the second tens, the third of the hundreds, the fourth the thousands, so ...
Examples: Given
number 673, the box contains the number of units 3 and then we have already accounted for 3 units (objects, houses, trees, dogs, books, computers ...), the box of ten has the number 7 which should be 7 units, but Since we must adhere to the specifications of our number system, the number seven is multiplied by 10, making 70. And so continuing, the build number.
sets of numbers are distinguished by the range and some properties. Are as follows:
- The set of natural numbers (N), which has as elements the numbers expressing quantities of natural , then from 0 (no amount or no amount) to infinity (∞).
- The set of integers (Z), also called for, with an interval (- ∞, + ∞), which has a 0 in the middle, before the zero mark with negative numbers - and after the zero with the positive sign + . In summary, the positive numbers we define quantities, while the negative amount that we lack (which do not have). (Ex: "I miss two apples" is equivalent to "I have apples -2).
- The set of rational numbers (Q), which numbers are represented by fractions.
- The set of real numbers (R) that brings together all the numbers represented.
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