_____ numbers are the rational numbers together with the irrational numbers. They are designated by ℝ
The numbers that are designated by ℝ are known as real numbers
The numbers that are designated by ℝ are known as real numbers. Real numbers include both rational numbers and irrational numbers combined.
Rational numbers can be expressed as a ratio of two integers, where the denominator is not zero. For example, fractions such as 2/3, -5/4, and 7/1 are all rational numbers. Rational numbers can also be whole numbers, integers, and terminating or repeating decimals.
On the other hand, irrational numbers cannot be expressed as a ratio of two integers. They cannot be written as fractions and have non-repeating, non-terminating decimal representations. Examples of irrational numbers are √2, π (pi), and e (Euler’s number).
When rational and irrational numbers are combined, we get all possible numbers on the number line, which form the set of real numbers denoted by ℝ. Real numbers are infinitely dense, meaning that between any two real numbers, there are infinitely many other real numbers. This set includes all fractions, decimals, integers, whole numbers, as well as numbers like √2 or π.
More Answers:
Understanding Monomials, Binomials, and Trinomials | Categorizing the Expression 3x + 0y as a Binomial.Understanding Rational Numbers | Exploring the Nature of 1/3
Understanding Irrational Numbers | A Complete Guide to Their Definition, Examples, and Applications.