Zero is an integer
Get to know whole numbers
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In these explanations you will learn how the set of whole numbers is structured and what properties the whole numbers have.
The set of whole numbers
You already know the natural numbers (). They can be represented (together with the zero) on the number line:If you extend the number line to the left beyond zero, you get a number line:While the natural numbers on the number line are plotted from left to right, this happens in the opposite direction for the new numbers to the left of 0. You therefore write a “-” (minus) in front of the number and call it negative numbers. The natural numbers are positive numbers and have a "+" (plus) sign. But you usually don't write that down.
Negative numbers in everyday life
The negative numbers differ from the positive numbers in that they have a minus sign. You also encounter negative numbers in everyday life.
When the temperature falls below it is given as a negative number:
If a place is below sea level, its location is indicated with "m and NN" (read: "meters below sea level"), or since the year 2000 with "muNHN" (read: "meters below sea level") .
If someone has incurred debts, these will be displayed as a negative number on the account: €
Whole numbers on the number line
The negative numbers are on the number line to the left of zero. You count from zero, so to speak, "backwards": 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, - 13, ...
The further to the left a number is on the number line, the smaller it is!
so is less than
Any negative number is less than zero and therefore also less than any positive number.
Amount and counterpart
The absolute value of a number is the distance from that number to zero.
There are two numbers that are the same distance from zero and therefore also have the same amount. Each of these two numbers is the opposite of the other.
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