Mathematical Induction

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Flashcards covering key concepts of Mathematical Induction based on lecture notes.

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10 Terms

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Principle of Mathematical Induction

A method used to prove mathematical statements for all positive integers.

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Base Case

The initial step showing that a statement holds true for n=1.

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Inductive Step

Assuming a statement is true for n=k and proving it for n=k+1.

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Inductive Hypothesis

The assumption that a statement is true for a specific positive integer k.

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Natural Numbers

The set of positive integers starting from 1.

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Divisibility

A condition where one integer can be divided by another without leaving a remainder.

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Summation

The operation of adding a sequence of numbers.

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Type 1 Question

A question that involves proving a statement about summation or multiplication of sequences.

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Type 2 Question

A question about statements involving divisibility by a natural number.

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Type 3 Question

A question that involves proving inequalities for positive integers.