Using different numbers by Stela Todorova

A number is a concept from mathematics, used to count or measure. Depending on the field of mathematics, where numbers are used, there are different definitions:

•. People use symbols to represent numbers; they call them numerals • People use symbols to represent numbers; they call them numerals. Common places where numerals are used are for labeling, as in telephone numbers, for ordering, as in serial numbers, or to put a unique identifier, as in ISBN is a unique number that can identify a book. • Cardinal numbers are used to measure how many items are in a set. {A,B,C} has size "3". • Ordinal numbers are used to specify a certain element in a set or sequence (first, second, third).

Numbers are also used for other things besides counting Numbers are also used for other things besides counting. Numbers are used when things are measured. Numbers are used to study how the world works. Mathematics is a way to use numbers to learn about the world and make things. The study of the rules of the natural world is called science. The work that uses numbers to make things is called engineering

Natural numbers

Natural numbers are the numbers which we normally use for counting Natural numbers are the numbers which we normally use for counting. Not all positive numbers are natural (for example ½ is positive, but not natural).

Negative numbers

Negative numbers are numbers less than zero. One way to think of negative numbers is using a number line. We call one point on this line zero. Then we will label (write the name of) every position on the line by how far to the right of the zero point it is, for example the point one is one centimeter to the right, the point two is two centimeters to the right.

Now think about a point which is one centimeter to the left of the zero point. We cannot call this point one, as there is already a point called one. We therefore call this point minus 1 (-1) (as it is one centimeter away, but in the opposite direction).

A drawing of a number line is below.

If they multiply two negative numbers together they get a positive number. For example -5 times -3 is 15. If they multiply a negative number by a positive number, or multiply a positive number by a negative number, they get a negative result. For example 5 times -3 is -15.

Integers

Integers are whole numbers Integers are whole numbers. This is all the natural numbers, all their opposites, and the number zero. Decimal numbers and fractions are not integers.

Rational numbers

Rational numbers are numbers which can be written as fractions Rational numbers are numbers which can be written as fractions. This means that they can be written as a divided by b, where the numbers a and b are integers, and b is not equal to 0.

A percentage is not totally a rational number but it has relationship with fraction and decimal. Sometimes, ratio considered as a rational number.

Irrational numbers

Irrational numbers are numbers which cannot be written as a fraction, but do not have imaginary parts. √2 is irrational

Irrational numbers often occur in geometry Irrational numbers often occur in geometry. For instance if we have a square which has sides of 1 meter, the distance between opposite corners is the square root of two. This is an irrational number. In decimal for it is written as 1.414213... Mathematicians have proved that the square root of every natural number is either an integer or an irrational number.

One well known irrational number is pi One well known irrational number is pi. This is the circumference of a circle divided by its diameter. This number is the same for every circle. The number pi is approximately 3.1415926359... . An irrational number cannot be fully written down in decimal form. It would have an infinite number of digits after the decimal point. These digits would also not repeat.

Real numbers

Real numbers is a name for all the sets of numbers listed above The rational numbers, including integers The irrational numbers This is all numbers but for imaginary numbers.

Imaginary numbers

Imaginary numbers are formed by real numbers multiplied by the number i. This number is the square root of minus one (-1). There is no number in the real numbers which when squared makes the number -1. Therefore mathematicians invented a number. They called this number i, or the imaginary unit.

Imaginary numbers were called imaginary because when they were first found many mathematicians did not think they existed. The person who discovered imaginary numbers was Gerolamo Cardano in the 1500s. The first to use the word imaginary number was René Descartes. The first people to use these numbers were Leonard Euler and Carl Friedrich Gauss. Both lived in the 18th century.