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Which set of numbers is not a subset of the rational numbers?
A set which contains any irrational or complex numbers.
Does every set have a proper subset?
No. The null set cannot have a proper subset. For any other set, the null set will be a proper subset. There will also be other proper subsets.
What is a complex set?
The set of complex numbers is the set of numbers which can be described by a + bi, where a and b are real numbers, and i is the imaginary unit sqrt(-1). Since a and b can be any real number (including zero), the set of real numbers is a subset of the set of complex numbers. Also the set of pure imaginary numbers is a subset of complex number set.
Set of real numbers and set of complex numbers are equivalent?
Real numbers are a proper subset of Complex numbers.
Is null set a proper subset of any set?
yes, if the set being described is empty, we can talk about proper and improper subsets. there are no proper subsets of the empty set. the only subset of the empty set is the empty set itself. to be a proper subset, the subset must be strictly contained. so the empty set is an improper subset of itself, but it is a proper subset of every other set.
What set of numbers does -0.002 belong to?
Rational (ℚ) which is a subset of Real (ℝ) which is a subset of Complex (ℂ).
What is the difference between a set of real numbers and a set of complex numbers?
The set of real numbers is a subset of the set of complex numbers. For the set of complex numbers, given in the form (a + bi), where a and b can be any real number, the number is only a real number, if b = 0.
Which set is a subset of every set?
The empty set is a subset of all sets. No other sets have this property.
Can any set be a proper set of itself?
NO- by definition a set is not a proper subset of itself . ( It is a subset, but not a proper one. )
Why is it that the null set is a subset of all sets?
-- The null set is a set with no members. -- So it has no members that are absent from any other set.
Is a null set is always a part of a universal set?
Yes. A null set is always a subset of any set. Also, any set is a subset of the [relevant] universal set.
Is pi a complex number?
The set of real numbers are a subset of the set of complex numbers: imagine the complex plane with real numbers existing on the horizontal number line, and pure imaginary existing on the vertical axis. The entire plane (which includes both axes) is the set of complex numbers. So any real number (such as pi) will also be a complex number. But many people think of complex numbers as something that is "not a real number".
