what is a cardinal set?

Cardinal numbers are counting numbers 1,2,3,4,  etc

If I wanted the set of cardinal numbers between 8.6 and 15.19 then the answer would be

{9, 10, 11, 12, 13, 14, 15}

So that is an example of a cardinal set.

However 

The cardinal number OF the above set is 7 because there are seven elements in the set.

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I would like another mathematician to comment on this answer.  I have done very little work with set notation etc.