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The complement of a set refers to everything that is NOT in the set. A "universe" (a set from which elements may be taken) must always be specified (perhaps implicitly). For example, if your "universe" is the real numbers, and the set you are considering is 0
Irrational numbers may be denoted by Q' since they are the complement of Q in R, the set of Real numbers.
It is if we only consider integers. If we consider all real numbers, for example, it would not be.
Only if they are fractions in their simplified form.
In a certain sense, the set of complex numbers is "larger" than the set of real numbers, since the set of real numbers is a proper subset of it.
The complement of a set refers to everything that is NOT in the set. A "universe" (a set from which elements may be taken) must always be specified (perhaps implicitly). For example, if your "universe" is the real numbers, and the set you are considering is 0
There is no representation for irrational numbers: they are represented as real numbers that are not rational. The set of real numbers is R and set of rational numbers is Q so that the set of irrational numbers is the complement if Q in R.
Irrational numbers may be denoted by Q' since they are the complement of Q in R, the set of Real numbers.
It is if we only consider integers. If we consider all real numbers, for example, it would not be.
real numbers
Only if they are fractions in their simplified form.
In a certain sense, the set of complex numbers is "larger" than the set of real numbers, since the set of real numbers is a proper subset of it.
the set of real numbers
Are disjoint and complementary subsets of the set of real numbers.
Real numbers are a proper subset 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.
Take any set; this set and its complement are mutually exclusive. Here are some examples:Negative and non-negative (i.e., positive and zero) numbersRational and irrational numbersIntegers and non-integersAlgebraic and transcendental numbersYou can also take a set and its complement from a smaller universe; these would also be mutually exclusive. For example:Even and odd numbers (only includes integers)