In the section of natural numbers, you will also encounter Cardinal Numbers. Cardinal numbers are also natural numbers but then what is the difference? Cardinal numbers measure the size of the sets. We call those sets cardinality of sets. It means a finite set of natural numbers which are placed according to their order.
The question is how cardinal numbers are helpful and why mathematicians found this important? Cardinal numbers help us to count a set of objects. For example, fifteen pencils, twenty-five coins, three pounds, three hundred and forty-five dollars, etc. It tells the quantity of specific things. Suppose you have two thousand and twenty-one pencils. Two thousand and twenty-one is referring to the quantity of pencils. That is why cardinal numbers are important. It doesn't show the order of the specific thing such as the second pencil is a blue pencil, etc.
Furthermore, like natural numbers, cardinal numbers cannot be in decimals or fractions. Speaking of fraction and decimal, you might be wondering can cardinal numbers be negative numbers? The answer is no because natural numbers follow counting numbers. All non-negative numbers are called counting numbers and since the cardinal number is a part of the natural number therefore we can conclude that cardinal numbers can't be a negative number, decimal, or a fraction. Last but not least, zero is also not a cardinal number because zero has no quantity and cardinal numbers define the quantity of the numbers.
| 1 one | 11 eleven | 10 ten | 100 one hundred |
| 2 two | 12 twelve | 20 twenty | 200 two hundred |
| 3 three | 13 thirteen | 30 thirty | 300 three hundred |
| 4 four | 14 fourteen | 40 forty | 400 four hundred |
| 5 five | 15 fifteen | 50 fifty | 500 five hundred |
| 6 six | 16 sixteen | 60 sixty | 600 six hundred |
| 7 seven | 17 seventeen | 70 seventy | 700 seven hundred |
| 8 eight | 18 eighteen | 80 eighty | 800 eight hundred |
| 9 nine | 19 nineteen | 90 ninety | 900 nine hundred |
| 1,000 one thousand | 10,000 ten thousand | 100,000 one hundred thousand | 1,000,000 one million |
| USA | Germany, Spain, France, ... | ||
| 1,000,000,000 | billion | thousand million (milliard) | |
| 1,000,000,000,000 | trillion | billion | |
| 1,000,000,000,000,000 | quadrillion | thousand billion (billiard) | |
| 1,000,000,000,000,000,000 | quintillion | trillion | |
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I’m afraid this article (on cardinal numbers) has an unfortunate error. Zero must be considered a cardinal number. The definition of a cardinal number given by the Penguin Dictionary of Mathematics is “A number that indicates the number of elements in a set.” It also defines a null set or empty set containing no elements. The cardinality of this set is 0.