The language of proof (HSC SSCE Mathematics Extension 2): Flashcards
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Practise the cards
10 cards from this deck
What is a mathematical proof?
What is a mathematical proof?
A logical argument establishing a proposition's truth.
Difference between theorems and conjectures?
Difference between theorems and conjectures?
Theorems are proven; conjectures are believed but unproven.
What does Pythagoras' Theorem state?
What does Pythagoras' Theorem state?
In a right triangle, c² = a² + b² for sides a, b, c.
What is the power of proof?
What is the power of proof?
Proofs provide permanent truths, unlike empirical evidence.
Why is precision important in proof language?
Why is precision important in proof language?
It avoids ambiguity and ensures clear understanding.
What defines an even number?
What defines an even number?
An even number is defined as 2k, where k is an integer.
What is an example of a logical statement?
What is an example of a logical statement?
If a number is even, dividing by 2 yields an integer.
What do quantifiers express in logic?
What do quantifiers express in logic?
They express universal or existential truths in statements.
What is the Collatz Conjecture?
What is the Collatz Conjecture?
A process involving even and odd numbers, unproven.
How is irrationality proven?
How is irrationality proven?
Through proof by contradiction, like with √2.