Why are the numbers on a ball in a lotto draw categorical nominal instead of categorical ordinal? Why are the number on a ball in a lotto draw categorical nominal instead of categorical ordinal?
Don't the numbers have a natural ascending order and would thus be ordinal? Or am I making an incorrect assumption about numbers having a natural order?
 A: You could color-code the balls without fundamentally changing the game. Instead of 6-12-11, we get red-blue-pink.
You could go with letters without fundamentally changing the game. Instead of 6-12-11, we get Y-Q-X.
You could use animal drawings without fundamentally changing the game. Instead of 6-12-11, we get dog-fish-horse.
The 6-ball isn’t worth half as much as the 12-ball. It doesn’t even represent a lesser value. The number is just on the ball as a link to lottery tickets.
It could be different if the number represented some kind of quantity, like rolling dice and advancing a game piece that many spots, but there’s nothing quantitative going on. The numbers on lottery balls just serve as links back to the tickets.
You probably can accept this for something like towns having zip codes or people having phone numbers. It’s the same idea.
A: The lines between the different types of variables are not as clear cut as we often define them. In many cases, the classification of a variables depends on how we use that variable instead of on the fundamental properties of the variable itself. Age in years and time measured in any fixed unit (days, hours, seconds) are good examples. These variables are fundamentally discrete (age in years falls in a countable set) but we often treat them as continuous in practice (e.g., regressing the probability of some disease on age as a continuous variable). 
I'd argue in this case that the numbers on the balls are an ordinal variable but if the order is not important in the lottery then we treat them as nominal. This makes the difference between numbered balls and coloured balls clearer. You could run the lottery differently so that the order of the balls matters (maybe you win if you match the highest number out of, say, four balls drawn at random). You can't do this with coloured balls (unless you impose an ordering like the wavelength of light). 
