Loading the lesson
Loading the lesson
Search AllRounder.ai
Search the courses, subjects, tracks, games and features, or jump straight to a page.
Search the courses, subjects, tracks, games and features, or jump straight to a page.
3 cards from this section. Quick, good the night before a test.
Provide a counterexample for the universal statement: 'All integers are positive.'
Remember an integer can be negative.
What does WLOG mean?
Think about simplifying cases in symmetrical arguments.
What is a counterexample used for?
Think about proving versus disproving.
True or False: A constructive proof provides no examples.
Recall what you understood about constructive proofs.
Consider the statement: 'If a number is positive, then its square is positive.' Use a proof by cases to discuss how one would validate this without explicit value examples.
Explore both positive and negative possibilities in numeric realms.
Demonstrate the non-constructive nature of proving that there are irrational numbers x and y such that xy is rational by using logical reasoning without establishing specific witnesses.
One valid path through exponentiation fulfilling conditions is your aim.
6 more questions in this section. Enroll free to practise them all.
Enroll free