Ordinal number

Ordinal numbers (or ordinals) are numbers that show something's order, for example: 1st, 2nd, 3rd, 4th, 5th.

Suppose a person has 5 different T-shirts, and then lays them in front of the person, from left to right.

• At the far left, there is the red T-shirt.
• Right of that is the blue one.
• Next to the blue is the green one.
• Then there is the yellow one.
• And finally, at the far right is an orange T-shirt.

If the person then starts counting the shirts from the left, he would first see the red shirt. So the red shirt is the first T-shirt. The blue shirt is the second T-shirt. The green shirt is the third one, the yellow T-shirt is the fourth one and the orange T-shirt is the fifth and the last T-shirt.

The first, second, third, fourth and fifth in this case are ordinal numbers. They result from the fact that the person has many objects, and they give them an order (hence 'ordinal'). The person then simply counts those objects, and gives the ordinal numbers to them.

In set theory, ordinals are also ordinal numbers people use to order infinite sets. An example is the set ${\displaystyle \omega _{0}}$ (or ${\displaystyle \omega }$ for short), which is the set containing all natural numbers (including 0).^[1][2] This is the smallest ordinal number that is infinite, and there are many more (such as ${\displaystyle \omega }$ + 1).^[3]

1. ↑ "Comprehensive List of Set Theory Symbols". Math Vault. 2020-04-11. Retrieved 2020-10-11.
2. ↑ "Cardinal and ordinal numbers". www.win.tue.nl. Retrieved October 10, 2020.
3. ↑ Weisstein, Eric W. "Ordinal Number". mathworld.wolfram.com. Retrieved 2020-10-11.