A number is a mathematical object used to count, label, and measure. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers.
Numbers for people
There are different ways of giving symbols to numbers. These methods are called number systems. The most common number system that people use is the base ten number system. The base ten number system is also called the decimal number system. The base ten number system is common because people have ten fingers and ten toes. There are 10 different symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) used in the base ten number system. These ten symbols are called digits.
A symbol for a number is made up of these ten digits. The position of the digits shows how big the number is. For example, the number 23 in the decimal number system really means 2 times 10 plus 3, and 101 means 1 times a hundred (=100) plus 0 times 10 (=0) plus 1 times 1 (=1).
Numbers for machines
Another number system is more common for machines. The machine number system is called the binary number system. The binary number system is also called the base two number system. There are two different symbols (0 and 1) used in the base two number system. These two symbols are called bits.
A symbol for a binary number is made up of these two bit symbols. The position of the bit symbols shows how big the number is. For example, the number 10 in the binary number system really means 1 times 2 plus 0, and 101
means 1 times four (=4) plus 0 times two (=0) plus 1 times 1 (=1). The binary number 10 is the same as the decimal number 2. The binary
number 101 is the same as the decimal number 5.
Names of numbers
English has special names for some of the numbers in the decimal number system that are “powers of ten”. All of these powers of ten numbers in the decimal number system use just the symbol “1” and the symbol “0”. For example, ten tens is the same as ten times ten, or one hundred. Also, ten hundreds is the same as ten times one hundred, or one thousand.
Types of numbers
Natural numbers are the numbers which we normally use for counting, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 etc. Some people say that 0 is a natural number, too. Another name for these numbers is positive numbers. These numbers are sometimes written as +1 to show that they are different from the negative numbers. If 0 is called a natural number, then the natural numbers are the same as the whole numbers. If 0 is not called a natural number, then the natural numbers are the same as the counting 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). All the normal operations of mathematics can be done with negative numbers.
Integers are all the natural numbers, all their opposites, and the number zero. Decimal numbers and fractions are not integers.
Rational numbers are numbers which can be written as fractions. This means they can
Rasyonel sayılar kesirli sayılar olarak yazılabilen sayılardır. Bu, a ve b tam sayı ve b0a
be written as a divided by b, where the numbers a and b are integers, and b is not equal to 0. A percentage could be called a rational number, because a percentage like 7% can be written as the fraction 7/100. It can also be written as the decimal 0.07.
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. For instance if we have a square which has sides of 1 meter, the distance between opposite corners is the square root of two, which equals 1.414213 … . This is an irrational number. 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. This is the circumference of a circle divided by its diameter. This number is the same for every circle. The number pi is approximately 3.1415926…
Real numbers is a name for all the sets of numbers listed above: The rational numbers, including integers and the irrational numbers.
This is all numbers that do not involve imaginary numbers.
Imaginary numbers are formed by real numbers multiplied by the number i. This number is the square root of minus one (-1).
They called this number i, or the imaginary unit. Imaginary numbers operate under the same rules as real numbers.
Complex numbers are numbers which have two parts; a real part and an imaginary part. Every type of number written above is also a complex number.
A real or complex number is called a transcendental number if it cannot be obtained as a result of an algebraic equation with integer coefficients. Well-known transcendental numbers: e, ?, ea