What is a natural number in math?
All children from an early age, studying mathematics. First, it allows you to learn simple things, easy to implement, but over time the tasks become more complicated. There is also a new terminology which is not always possible to understand what is meant. For example, what is a natural number in math?
In ancient times people did not use numbers like you’re doing now, but still they required. The items were compared to the number of something, for example, someone who has had so many berries, how many fingers on one hand. Gradually, people invented a system account, and with it came new terms.
What is a natural number in math?
This concept is one of the oldest, as it was born because of a long-standing need to learn how to count the number of normal subjects. That means a natural number? Most often given this definition – it is the numbers that arise in counting, and this happens naturally.
It takes its second name of this term are natural numbers. Their sequence, location of growth, they form a natural series. In other words, all digits starting with the units that are used to count objects that are natural.
Thus, there is a smallest natural number – they have one. The biggest is not the case, as any one may add another one. Zero is not included in a natural number, because with it, there is nothing to count, although not all scientists agree with this.
The definition of natural numbers
These figures are determined by two main methods. The first one involves the enumeration of all available, and the second calls the final number.
- The first method definition is a counting or numbering of existing items. For example, seeing before him a few apples, the man can count them – one, two, three…
- The second method of determining the total number of calls to the available items. Thus, if there are no apples at all, then we can say that items no. This means that when counting, you receive a zero.
This figure is the main difference between these two methods of definition. In the first case the minimum number is the unit, and the second and possibly the use of zero. Mathematics was unable to reach a unanimous decision about what method is better and is it worth it to put a zero on a par with other natural numbers.
Usually used the first option, leaves a controversial figure in the side. However, in some works, like Bourbaki, uses a different approach. In addition, zero is an integral and widely used part in the world of programming.
Features of natural numbers
The main thing you need to remember when referring to such numbers, so it is their duty to be natural. They must be such that with their help it was possible to count the number of some items. Natural numbers should be accessible and understandable for all.
For this reason, they do not include negative indicators and different non-integer number. For example, the rational, denoted by the fraction, or float, is a mathematical object, can not become a part of the natural numbers.
What is a natural number in math? All these figures are denoted by the letter N. It was chosen because in Latin the word natural spelled as naturalis, that is, starts with the letter N. the Number that is meant by this designation indefinitely.
Often to prove complex theorems, it is useful to remember zero. It is included in the extended natural number, which is denoted with the corresponding numerals assigned below to the letter N. Sometimes used instead of Z, again with the same small close to zero.
Operations with natural numbers
In mathematics there is the concept of closures. It means the minimal extension of a set, operations which do not go beyond it. Regarding the natural numbers there are several such closed operations.
- Primarily, this Addendum. Natural numbers can be easily folded with each other to get some money.
- Perhaps multiplication. Two natural multiplier will give you work.
- Finally, use the exponentiation. It consists of a base and indicator. In that case, if both parts are represented by natural numbers, the result will be the same.
Sometimes this question deals with two more operations. Their problem is that they do not apply to all cases. Sometimes these can exist and sometimes not. These operations include:
- Subtraction. It will give a natural number only if the first digit is greater than the second. Otherwise, it is possible to obtain negative numbers, which is not true for natural or zero, which is controversial;
- The same is true for division. In the simplest examples all numbers in the end will be natural, however, there are many situations in which work is unwhole.
As a rule, science focuses on the first two operations – addition and subtraction. I wonder what they contribute to the creation of the ring of integers is going through a binary addition and multiplication.
What you should know about the natural numbers?
The numbers used for counting were not always such as we know them today. First used a relatively schematic representation, gradually formed in Roman numerals.
The modern version originated in India about fifteen hundred years ago. Subsequently, they were brought to European countries by Arabs, for which he received his famous name – Arabic numerals. Despite the fact that natural numbers can be any number, all ten digits from zero to nine.
If we consider a natural number, each number will differ from the preceding or subsequent per unit, despite the fact that the number is infinite. However, in the process of counting there is a so-called decimal position.
This word refers to the fact that when the numbers reach ten, they form a new unit high order. These discharges are very different – in particular, these include the millions and billions. Depending on their quantity digits to combine classes.
For example, billions can amount to tens or hundreds. It will be level, but they generally form a class billion. The same thing happens with the digits of millions, thousands, hundreds, tens and units.