The symbols that we now use to indicate the number were invented by the smart and resourceful people of India more than 15 centuries ago. Our ancestors learned about them from the Arabs, who began to use them before others.
What is the difference between a number and a number? The figure comes from the Arabic language and has the direct meaning of “zero” or “empty space”. In total there are 10 digits, which, in turn, combining in different ways, make up the numbers.
The difference between numbers and numbers
In order to understand what is the difference between the concepts of "number" and "number", you need to remember the following postulates:
- The numbers are only ten: zero, one, two, three, four, five, six, seven, eight, nine. All other combinations are numbers.
- A number is an integral part of a number. How many digits are there in number? There may be a different number of them.
- Each digit is a sign, symbol. Any number is a quantitative abstraction.
Arab Sifra
The number as a word has Arabic roots.
Initially in Arabic, it was the word "siphra," that is, "zero." The numbers are some symbols that indicate numbers. The numbers are indicated as follows:
- 0 is zero;
- 1 - one;
- 2 - two;
- 3 - three;
- 4 - four;
- 5 - five;
- 6 - six;
- 7 - seven;
- 8 - eight;
- 9 - nine.
The above numbers are called Arabic.
Roman numeral system
The Arab numeral system in the world is not one. There are other systems. Each of them is completely different from the other.
For example, in addition to the Arab system, the Roman system of counting is very popular. But Roman numerals are spelled differently and do not resemble Arabic.
- I is one;
- II- two;
- III - three;
- IV - four;
- V- five;
- VI - six;
- VII - seven;
- VIII - eight;
- IX - nine;
- X is ten.
As you may have noticed, there is no symbol for zero. So as a figure, you can take the top ten.
Number systems
The number system is a kind of representation of numbers.
For example, imagine that you have several apples in front of you. Would you like to know how many apples are on the table? To do this, you could count by bending your fingers or making nicks on a tree. And could you imagine that ten apples is one basket, and one apple is one match. Spread matches on the table under one.
In the first version of the calculation, the number turned out as a string of nicks on a tree (or bent fingers), and in the second version of the calculation, it was a set of baskets and matches. There should be tanks on the left, and matches on the right.
Number systems are of two types:
- Positional
- Non-positional.
Positional number systems are:
Non-positional is called such a number system in which the number in the number correlates with a quantity that does not depend on its category. Therefore, if you have five notches, then the number will be five. For each notch will correspond to one apple.
A positional number system is one in which the number in a number will depend on its rank.
The number system we are used to is the decimal system of counting. She is positional.
When our ancestors began to learn to count, they got the idea to write numbers. initially they used the very nicks on trees or stones, where each dash denoted an object (one apple, for example). That is how the single number system was invented.
Single number system
The difference between a digit and a number in the unit number system is that the number in this case is equivalent to a string consisting of sticks. The number of sticks (notches on the tree) is equal to the value of the number.
For example, a crop of 50 apples will be equal to a number consisting of 50 sticks (dash, nick).
How many digits does the number 50 contain? Two numbers. The number 0 and the number 5. But the number of apples is much more than two.
The main disadvantage in this number system is a too long line of dashes. And if the harvest was 5,000 apples? Indeed, writing such a number is inconvenient. Reading will also be difficult.
Therefore, later our ancestors learned to group dashes in several pieces (5, 10 each). And for each unifying group a special sign was invented. First, fingers 5 and 10 were used. And then certain characters were invented. In this way, counting apples has become much easier.
Ancient Egyptian Decimal Number System
The ancient Egyptians began to use special characters to indicate numbers. Even ancient people understood the difference between a number and a number.
Numbers:
1, 10, 10 2 , 10 3 , 10 4 , 10 5 , 10 6 , 10 7 .
So, the ancestors learned to group different signs (symbols). The Egyptians chose the number ten for their group, without changing the number one.
In this particular example, the number ten is the base of the decimal number system. And each character in this number system is the number 10 to some extent.
The Egyptians wrote down numbers combining these signs (symbols). If the number was not a power of ten, all missing characters were added by repetition. Each character could be repeated no more than nine times. The result was equal to the sum of the elements of the number.
Binary number system
This number system is currently used in computer technology. The decimal number system is inconvenient for those machines that serve people today.
The binary number system uses only two digits:
Only one digit is allowed in each category - either 0 or 1. To convert a number from binary to decimal, you will need to multiply all the numbers in turn by base 2, which is raised to a power equal to the category.
Octal number system
The octal number system is also often applicable in modern electronics. As you understand, only eight digits are used here.
- 0 is zero;
- 1 - one;
- 2 - two;
- 3 - three;
- 4 - four;
- 5 - five;
- 6 - six;
- 7 - seven.
To translate a number into a decimal number system, you need to multiply each digit of a given number by 8 (to the degree of a digit) .
Hexadecimal digits
Programmers and people whose profession is closely related to computer machines use the hexadecimal number system.
- 0 to 0;
- eleven;
- 2 to 2;
- 3 to 3;
- 4 to 4;
- 5 to 5;
- 6-6;
- 7 to 7;
- 8 to 8;
- 9 to 9;
- A is 10;
- B is 11;
- C is 12;
- D is 13;
- E is 14;
- F - 15.
Number and number
Number is a concept that refers to quantity.
A number is a symbol or sign that denotes a number.
The number of digits in a number can be different, from one to infinity.
For example, the number "seven" is given, which reflects the amount of something. But this is the very number we write with the number 7.
The definition of numbers and numbers in simple language is given below.
Numbers are necessary in order to keep track of any objects, measure length, measure time, speed and other quantities. A number is a symbol that shows the number visually, clearly and visually.
Roughly speaking, a figure can be compared with a letter from the alphabet, and a word with a number. That is, there are only 33 characters in the Russian language to denote letters. With their help, you can record as many words as you like. And there are only ten digits to indicate numbers.
Let's clearly understand how a digit differs from a number.
In order to write the number 587, we will use three digits: 5, 8 and 7. By themselves, the numbers cannot in any way reflect an integer. With the same numbers, we can write many more different numbers. For example, 857, 875 878755 and so on.
When to use the "number", and when - the "number"?
If a person says: “Please write down the number 7. Now add 8 to it.” This option will be considered competent and correct.
If they say to you: “Write down the number 9. And take away 3”, this is wrong and illiterate. Something cannot be taken away from the figure. Just like from a letter, for example. This is just a symbol, how can a certain amount be subtracted from it? It will be correct: "Write the number 9 ...".
The option "Write down the number 23" is also incorrect. Such a figure simply does not exist. There is a number 23, which can be written in numbers 2 and 3.
Who cares ?
So, without an account, we cannot imagine our life. This is undeniable. In our world there is no way to live without numbers and numbers. But we rarely think about what we are dealing with now - with a number or with a number.
As we already found out earlier, a digit is just a symbol, a sign that is customary to be used to indicate something.
A number shows the amount of something with the help of these same signs - numbers.
A number can be not only an integral part of a number, but also a number, more precisely, its analogue. Of course, provided that it denotes the number of items up to and including 9.
Main findings
So, what is the difference between a number and a number:
- Numbers - this is a certain unit of account from zero to nine inclusive. All other combinations of numbers are numbers.
- How many digits in a number denoting the same quantity depends on the number system.
- Each number is created from numbers.
- The main difference between numbers and numbers is that the first concept is abstract, it is just a symbol, and the second expresses the amount of something.
- The number and number vary depending on the number system. One and the same number may indicate a different number.