What are number levels to letter levels

What are the numbers?

In mathematics we calculate with numbers. A distinction is made between different types of numbers (classes). The most important types of numbers are:




to natural numbers

Natural numbers are the numbers 1, 2, 3, 4, 5, 6, 7, 8, ..., i.e. those that everyone needs to count. In principle, everything I can count is called a natural number.

As you can see, the "0" is missing in the above list. Some mathematicians add the “0”, but others don't.

The set of natural numbers is indicated by the symbol abbreviated.
It includes either the positive whole numbers

or the nonnegative integers



Together with addition and multiplication, the natural numbers form a mathematical structure. The natural numbers can be further subdivided. There are also the even numbers, the odd numbers, and the prime numbers.
Even numbers are all numbers that can be divided by 2 without a remainder. These are the numbers 2, 4, 6, 8, 10, 12 ...
The odd numbers are in between: 1, 3, 5, 7, 9, 11 ...
The so-called prime numbers, on the other hand, can only be divided by themselves and by 1 without a remainder. The first prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 ...

In addition, there are the terms "cardinal number" and "ordinal number", which are not so important to us at the moment. If you want to know more, please google it.

to whole numbers

A whole number is all numbers that have only zeros after the decimal point. Examples:…. -4, -3, -2, -1, 0, 1, 2, 3, 4 ...

The amount is called the set of whole numbers.

The whole numbers contain all natural numbers including the zero and all these numbers with a minus sign in front of them. The set of integers is totally ordered, in order

d. H. you can compare two whole numbers. One speaks of positive, nonnegative, negative and non-positive whole numbers.
The number 0 itself is neither positive nor negative.
This okay is compatible with the arithmetic operations, d. H.
is and , then ,
is and , then .
Like the set of natural numbers, the set of whole numbers is also countable.

too negative numbers

The negative numbers arise when you subtract a larger number from a number.
All numbers consist of two parts, the amount and the sign.
Annotation:
The amount are the "normal" numbers. When talking about the amount of a number, put the number between 2 dashes, e.g. I2I means "amount of 2"

The sign is either + (plus, and is usually not written) or - (minus).
Negative numbers are e.g. -1, -2, -3, -4, ....... etc.

Note: Be careful here !!
Example: what is 10-35?
Since 35 is greater than 10, that is not really possible. So let's first turn the numbers around:
That means we calculate 35 -10, that results in 25 and we call that "amount".
We now write the sign in front of this amount: -25 is the end result of 10 - 35:



to rational numbers

Every rational number is a real number that can be represented as the ratio of two whole numbers. One also speaks of a “fractional number”. The set of all rational numbers is given by the symbol (from "quotient").
The amount is called the set of rational numbers.
It includes all numbers that can be represented as a fraction that contains whole numbers in both the numerator and the denominator.
However, there must never be a “0” in the denominator. Division by zero is not permitted for us.
For example, rational numbers are: 1/2, 1/3, 4/6, 167/346 ... etc.

too irrational numbers

Rational numbers can be represented as a fraction, but irrational numbers cannot be represented as an integer fraction!
Therefore one can define:
Irrational numbers are all point numbers that cannot be represented as a fraction. These are mostly numbers that come about through infinite sequences and series (such as the number Pi).
For example, if you take the root of the number 2, you get about 1.4142. However, this number is imprecise, because the root of 2 has an infinite number of digits after the decimal point. This also applies to the circle number π (pronounced: pi), for which the value 3.14 is usually used as an approximation in schools. In practice you break off after a certain place after the comma and thus get a finite decimal number (point number).


too real numbers

If you combine all the rational and irrational numbers into a set, you get the so-called real numbers.
The set of real numbers corresponds to the set of all points on the number line. The symbol becomes their designation used.

The real numbers are divided into:

a) rational numbers


b) whole numbers


c) natural numbers= or =


d) irrational numbers = the set of all elements of that are not in lie. These can in turn be divided into:
irrational algebraic numbers and transcendent numbers.



too complex numbers

Complex numbers are only calculated at universities of applied sciences or technical universities, preferably if you have a Dipl.Ing. for electrical engineering.
The complex numbers expand the Number range of real numbers such that the equation becomes solvable.
This is achieved by introducing a new number with the property . This number is called an imaginary unit. In engineering, the letter used to avoid confusion with a (by designated) from the time to prevent dependent current strength.