Types of Sets

Algebraic

The intersection of two algebraic sets is an algebraic set corresponding to the union of the polynomials. For example, and intersect at , i.e., where and .

Complex

Complex training is a workout comprising of a resistance exercise followed by a matched plyometric exercise e.g.: squats followed by squat jumps bench press followed by plyometric press up

Imaginary

An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i 2 = −1. The square of an imaginary number bi is −b 2. For example, 5i is an imaginary number, and its square is −25. Zero is considered to be both real and imaginary.

Integer

Other integer data types are implemented with a fixed size, usually a number of bits which is a power of 2 (4, 8, 16, etc.) or a memorable number of decimal digits (e.g., 9 or 10). Cardinality The cardinality of the set of integers is equal to ℵ 0 .

image: socratic.org
Natural

For example, it is intuitive from either the list {1, 2, 3, 4, ...} or the list {0, 1, 2, 3, ...} that 356,804,251 is a natural number, but 356,804,251.5, 2/3, and -23 are not. Both of the sets of natural numbers defined above are denumerable. They are also exactly the same size.

Rational

The term rational in reference to the set Q refers to the fact that a rational number represents a ratio of two integers. In mathematics, "rational" is often used as a noun abbreviating "rational number". The adjective rational sometimes means that the coefficients are rational numbers.

Real

There exist sets of real numbers that are not Lebesgue measurable, e.g. Vitali sets. The supremum axiom of the reals refers to subsets of the reals and is therefore a second-order logical statement. It is not possible to characterize the reals with first-order logic alone: the Löwenheim–Skolem theorem implies that there exists a countable dense subset of the real numbers satisfying exactly ...

image: ebay.com