Practice - Common Mistakes in Proof by Induction
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Practice Questions
Test your understanding with targeted questions
What is the purpose of the base case in proof by induction?
💡 Hint: Think about where the induction starts.
What is the inductive step in induction?
💡 Hint: What transition do we make from k to k+1?
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the first step in a proof by induction?
💡 Hint: What step do we always begin with in the induction framework?
True or False: Strong induction requires proving the property for all preceding integers.
💡 Hint: What makes it 'strong' compared to regular induction?
1 more question available
Challenge Problems
Push your limits with advanced challenges
Prove by induction that for all integers n, 3^n > n^3 for n >= 3.
💡 Hint: Use properties of exponential functions and inequalities.
Show using strong induction that every integer greater than 1 can be expressed as a product of prime numbers.
💡 Hint: Consider prime factorization and how primes build numbers.
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