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SubjectsMathematics
रिक्त समुच्चय से अनंत समुच्चय तक: चरण 3
This Class 10 Mathematics topic from the chapter Sets explains the concluding step used to show that a set is infinite. Students distinguish an empty set, which contains no elements, from an infinite set, whose elements do not end, and follow how a logical argument supports this conclusion. The topic strengthens understanding of set notation, membership, and mathematical reasoning, helping learners interpret why the existence of continually extendable elements rules out a finite count.
TOPIC PRACTICE
Up to 3 questions from this page. Select your focus, then start.
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.
Taking n = 1, 2, 3, 4, and so on produces the distinct values 1, 1/2, 1/3, 1/4, and so on. Although these positive fractions become smaller and approach zero, they never become zero and the process of choosing a new natural number never ends. Thus the set has infinitely many elements, so option C is correct.
Set A contains all numbers greater than 1 up to and including 5. Set B contains all numbers from 5, including 5, up to but not including 9. The only number common to both sets is 5. Hence their intersection is the singleton set {5}, not an interval extending on either side of 5.
QUIZ COMPLETE
