An ordinal number tells you where something is in a sequence of things. For example the sixth house on a street, the third row of seats. The word is derived from the idea of 'order'. When things are arranged in some known order, then the ordinal is the position in that sequence.

For this to work, we must know the way the items are ordered. For example if we arrange children by age, then child 1 (the first one) is the youngest, followed by child 2 and child 3 etc. These "child numbers" are the ordinal numbers of the set of children when put in age order.

If we put the children in height order, then child one (the first one) would be the shortest etc.

Road example

As we drive along many major roads we see that the junctions are often numbered. The designers start at one end and the first intersection (junction) is numbered one, then two etc.

In the above example, starting on the left (west) end of the road there are five junctions. So the first junction is junction 1, the second is junction 2 etc. These "junction numbers" are the ordinal numbers of the junctions.

Arithmetic with ordinal numbers

There is a limited way that ordinal numbers can be worked with arithmetic. For example if I tell you to go to junction 2, then go three more junctions, you can take the 2, add 3 and get junction 5. Aside from situations like this, there is little meaningful arithmetic that can be done with ordinal numbers.

Other number topics

Scalar numbers

Counting numbers

Numbers that have factors

Special values