What is the difference between cardinal and ordinal numbers?
short answers for big questions
Numbers can be classified as being ordinal or cardinal. Cardinal numbers are useful to answer some kinds of questions like “How many fish are there in the fishbowl?” or “How much money do I have in the bank?” So, they are used to count. Regarding the ordinal numbers, they are used to establish an order or hierarchy, that is, to show the position of something in a list. If you read sentences like “I won the first prize of Maths” or ”My son was the third in the run”, the numbers first and third are examples of ordinal umbers.
It seems to be easy: could you give one more example?
Having in mind the above examples we could say that the difference between ordinal and cardinal numbers seem to be obvious. However, it can sometimes be more subtle. Let’s see the following example: “June has 30 days”. In this case number 30 means a cardinal number since it is used to count the total of days of June. But if we read a sentence like “I’m having a drive examination on the 30th of June”, number 30 stands for an ordinal number since we are showing that the exam is going to take place on the thirtieth of June.
And what is the cardinal of a set: is it connected to what you said before?
Yes, it is. We have previously explained that cardinal numbers were used to count. So, the cardinal of a set stands for the number of elements of a set. In Maths there is even a symbol for that – the symbol `#` (cardinal). According to the picture below we have a set of geometric figures, that we will give the name set `A`. So, we can say that `#A = 4`.
What is the correspondence between cardinal and ordinal numbers?
So as to be easier to answer this question, I’ll show you a table containing some examples.
Cardinal and Ordinal numbers
| Cardinal | Ordinal | Cardinal | Ordinal | Cardinal | Ordinal |
|---|---|---|---|---|---|
| 1 | first | 9 | ninth | 70 | seventieth |
| 2 | second | 10 | tenth | 80 | eightieth |
| 3 | third | 11 | eleventh | 90 | ninetieth |
| 4 | fourth | 20 | twentieth | 100 | one hundreth |
| 5 | fifth | 30 | thirtieth | 200 | two hundredth |
| 6 | sixth | 40 | fortieth | 300 | three hundreth |
| 7 | seventh | 50 | fiftieth | 1000 | one thousandth |
| 8 | eighth | 60 | sixtieth | 1000000 | one milionth |
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