Choose the correct statement about the set of irrational numbers between 0 and 1.
Answer and explanation
Correct answer: It is infinite
There are irrational numbers strictly between 0 and 1; for example, √2/2 is approximately 0.707 and is irrational. Moreover, infinitely many distinct irrational numbers lie in this interval. For instance, the density of irrational numbers in the real numbers guarantees irrational numbers between any two different real numbers. Thus the set is infinite, and option D is correct.
Frequently asked questions
What is the correct answer to this question?
It is infinite
Why is this the correct answer?
There are irrational numbers strictly between 0 and 1; for example, √2/2 is approximately 0.707 and is irrational. Moreover, infinitely many distinct irrational numbers lie in this interval. For instance, the density of irrational numbers in the real numbers guarantees irrational numbers between any two different real numbers. Thus the set is infinite, and option D is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, many more. Step 3: Hence the set is infinite..
