0
"Densest" is not really an applicable term here. I take it you mean "has the highest cardinality?" In this cast there are an infinite number of these. A theorem states (I forget the name) that a subset of a set can have at most the same cardinality of that set. So we need a set S such such that S ⊆ ℝ and |S| ≈ |ℝ|. Like I said, many sets fit this description, i.e. ℝ itself, any open or closed interval on ℝ like [1,16) or (-∞, 3), any union of any subset of ℝ and an open or closed interval on ℝ such as (12, ∞) ∪ {e}. I suppose that there are many types that I may be forgetting, but I hope you understand. =]
Still curious? Ask our experts.
Chat with our AI personalities
Rafa
Coach
ProfessorAdd your answer:
Earn +20 pts
Is the densest subset of real numbers is set of fractions?
No, the irrationals are more dense.
Is fraction the densest subset of real numbers?
No. Fractions do not include irrational numbers. And although there are an infinite number of both rationals and irrationals, there are far more irrational numbers than rationals.
Is real numbers a subset of Integers?
You have it backwards. Integers are a subset of real numbers.
Which is the largest subset of a real numbers?
The real numbers, themselves. Every set is a subset of itself.
What are the hierarchy of real numbers?
Starting at the top, we have the real numbers. The rational numbers is a subset of the reals. So are the irrational numbers. Now some rationals are integers so that is a subset of the rationals. Then a subset of the integers is the whole numbers. The natural numbers is a subset of those.
