Each of the following is a subset of the real numbers: -- the odd numbers
-- the even numbers
-- the numbers greater than 4
-- the numbers containing the digit '7'
-- the abcissas of points in the 3rd quadrant
-- the first 269 multiples of 'pi'
-- the number of fish in each of the Seven Seas
-- the numbers that have the letter 'L' in their English names
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Rational (ℚ) which is a subset of Real (ℝ) which is a subset of Complex (ℂ).
Yes.
A set of ordered pairs (x, y) where x and y are real numbers.
Yes. For example, the set of odd natural numbers is a infinite subset of the set of integers.
A set which contains any irrational or complex numbers.