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What is the set of numbers including all irrational and rational numbers?
real numbers
What is A set of numbers that is larger than the set of real numbers?
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.
What is the set of numbers that includes all rational and all irrational numbers?
the set of real numbers
The set of all rational and irrational numbers?
Are disjoint and complementary subsets of the set of real numbers.
Set of real numbers and set of complex numbers are equivalent?
Real numbers are a proper subset of Complex numbers.
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.
Why do you think there are different set of real numbers?
There is only one set of Real numbers.
Does a real number contain the set of rational numbers?
No. A real number is only one number whereas the set of rational numbers has infinitely many numbers. However, the set of real numbers does contain the set of rational numbers.
The densest subset of real numbers is the set of fractions?
Your question is ill-posed. I have not come across a comparison dense-denser-densest. The term "dense" is a topological property of a set: A set A is dense in a set B, if for all y in B, there is an open set O of B, such that O and A have nonempty intersection. The rational numbers are indeed dense in the set of real numbers with the standard topology. An open set containing a real number contains always a rational number. Another way of saying it is that every real number can be approximated to any precision by rational numbers. There are denser sets, if you are willing to consider more elements. Suppose you construct a set consisting of the rational numbers plus all algebraic numbers. The set of algebraic numbers is also countable, but adding them, makes it obviously easier to approximate real numbers. Can you perhaps construct a set less dense than the set of rational numbers? Suppose we take the set of rational numbers without the element 0. Is this set still dense in the real numbers? Yes, because 0 can be approximated by 1/n, n>1. In fact, you can remove finite number of rational numbers from the set of rational numbers and the resulting set will still be dense in the set of the real numbers.
How are rational numbers and integal numbers related to set of real numbers?
Both rational numbers and integers are subsets of the set of real numbers.
Set of real numbers?
The set of real numbers is the union of the set of rational and irrational numbers. But there are so many other ways to describe it. Real numbers can be constructed as Dedekind cuts of rational numbers. The set of real numbers can also be viewed as the set of equivalence classes of Cauchy sequences of rational numbers Some people like the definition, that the real numbers are all the numbers which can be expressed as decimals.
What is a set of rational and irrational numbers?
It is the set of Real numbers.
