I'm not sure if this is what you're looking for: Real numbers greater than zero. Includes rational and Irrational Numbers.
Rational positive numbers
The set of numbers that consists of the positive numbers, the negative numbers, and zero are integers. There are no fractions in integers.
It is the set of all numbers excluding zero.
The set of integers, the set of rational numbers, the set of real numbers, the set of complex numbers, ...
Natural numbers are just whole positive numbers. Since whole positive numbers can represent a distance along a line, they are a subset of real numbers.
Rational positive numbers
The set of numbers that consists of the positive numbers, the negative numbers, and zero are integers. There are no fractions in integers.
The set of counting (natural) numbers is the set of all positive integers, while the set of whole numbers is the set of all positive integers included zero.
It is the set of all numbers excluding zero.
The set of integers, the set of rational numbers, the set of real numbers, the set of complex numbers, ...
Natural numbers are just whole positive numbers. Since whole positive numbers can represent a distance along a line, they are a subset of real numbers.
integer
Some integers are positive numbers.Some integers are not positive numbers.Some positive numbers are integers.Some positive numbers are not integers.They are two sets whose intersection is the set of counting numbers.
No.
The set of integers (ℤ) is the set of the positive whole numbers and their additive opposites (the negative whole numbers).
Easily. Indeed, it might be empty. Consider the set of positive odd numbers, and the set of positive even numbers. Both are countably infinite, but their intersection is the empty set. For a non-empty intersection, consider the set of positive odd numbers, and 2, and the set of positive even numbers. Both are still countably infinite, but their intersection is {2}.
A set can be anything. {1, 2, 3} is a set of the first 3 counting numbers. It's also the first three positive integers. The the set of the smallest positive whole numbers.