Well, isn't that just a happy little mistake? It looks like the number 729 doesn't quite fit in with the others. Just like in painting, sometimes things stand out in their own unique way, and that's okay!
Irrational numbers.
None. There is nobody to whom triangular numbers belong.
Rational numbers.
mixed numbers
No, they can belong to infinitely many subsets.
The set of numbers which 3 does not belong is the set of even numbers.
10 belongs to the set "natural numbers", but it can also belong to whole numbers, and rational numbers
Counting numbers
Rational numbers
Irrational numbers.
odd numbers, perfect square numbers
None. There is nobody to whom triangular numbers belong.
Rational and Real numbers
rational and prime numbers
Rational numbers.
mixed numbers
No, they can belong to infinitely many subsets.