Can nominal data have uncountably many values?
Are categorical data the same as nominal data?
Are discrete data the same as nominal data?
Thanks!
Let's see:
1) I think it depends on how you mean "uncountably". In a strict sense, no. You could count every atom in the universe, at least in theory. But in a more practical sense - sure. A list of all possible molecules is finite but it's so big that the finiteness is not practical.
2) Categorical data can certainly be nominal; they can also be ordinal (e.g. opinions given on a Likert scale). You can even categorize (and people frequently do) data that is interval or ratio, and sometimes you can uncategorize it.
3) As @Gung pointed out, a count variable is discrete but not categorical. They are also not nominal - indeed, counts don't fit perfectly into Stevens' classification - they are discrete but ratio, in that e.g. a person with 3 cars has 3 times more than a person who has 1.