Practice - Universality of the Statement
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
What is a subsequence?
💡 Hint: Think of sequences like (1, 3, 2). Which numbers can form a subsequence?
Define a strictly increasing sequence.
💡 Hint: Consider the sequence (a, b, c) — what should a be compared to b?
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is a strictly increasing subsequence?
💡 Hint: Think of an example where this applies.
True or False - Every sequence of 5 distinct real numbers contains a subsequence of length 5 that is either increasing or decreasing.
💡 Hint: Reflect on the definition of subsequences.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Prove the statement with a specific example of seven distinct real numbers.
💡 Hint: Arrange numbers visually to help identify patterns.
Demonstrate the pigeonhole principle clearly with 10 numbers and 3 distinct categories (such as odd, even).
💡 Hint: Digging into the counts will help clarify.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.