the seat of real number is the union of the set of irrational number true or false?
Use the article for which you got a link (on your next question) and note that whole numbers belong to the set of rational numbers, for example,
5=5/1=10/2,etc, which are all rational numbers.
I believe the question has a typo (parts missing).
True.
To understand why the statement is true, let's break it down:
The set of real numbers (denoted as ℝ), consists of two main types of numbers: rational numbers and irrational numbers.
- Rational numbers are numbers that can be expressed as a fraction p/q, where p and q are integers and q is not equal to zero. Examples of rational numbers include 1/2, 3/4, -2/5, etc. Rational numbers can be written as a finite decimal or as a repeating decimal.
- Irrational numbers, on the other hand, are numbers that cannot be expressed as a fraction. They have non-terminating and non-repeating decimal representations. Examples of irrational numbers include π (pi), √2 (the square root of 2), e (Euler's number), etc.
Now, the statement says that the seat (or the set) of real numbers is the union of the set of irrational numbers. In other words, all irrational numbers are also real numbers.
This statement is true because the set of real numbers contains both rational and irrational numbers. So when we take the union of the set of irrational numbers with the set of rational numbers, we get the entire set of real numbers.
In mathematical notation: ℝ = Q ∪ I, where Q represents the set of rational numbers, I represents the set of irrational numbers, and ∪ denotes the union of two sets.
Therefore, the statement that the set of real numbers is the union of the set of irrational numbers is true.