Proving divisibility by induction (HSC SSCE Mathematics Extension 1): Flashcards
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What is mathematical induction used for?
What is mathematical induction used for?
To prove statements for natural numbers.
Define divisibility in integers.
Define divisibility in integers.
N is divisible by d if N = d × q for some integer q.
What is the closure property in integers?
What is the closure property in integers?
Results of adding, subtracting, or multiplying are integers.
Why is the closure property important?
Why is the closure property important?
It helps set up proof structures in induction.
What is a base case in induction?
What is a base case in induction?
The starting point to prove a statement is true.
What is the inductive step?
What is the inductive step?
Assume true for n=k, prove for n=k+1.
What must be shown in the inductive step?
What must be shown in the inductive step?
That the statement holds for n=k+1.
What ensures results remain integers in induction?
What ensures results remain integers in induction?
Integer closure in divisibility.
What is a common error in induction?
What is a common error in induction?
Incorrect base case initialization.
How do practice problems enhance math skills?
How do practice problems enhance math skills?
They reinforce concepts and improve problem-solving abilities.