Question

Difference between strong induction and mathematical induction

Answer 1

Answer:

By simple induction

you use "if f(x) is true then f(x+1) is true"

while in strong induction

you use "if p(i) is true for all i less than or equal to k then f(x+1) is true", where f(x) is some statement depending on the positive integer k. They are NOT "identical" but they are equivalent

Step-by-step explanation:

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Answer 2

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In standard induction, we assume that a statement is true for a certain number [math]k[/math], then we use that assumption to show that it is true for [math]k+1[/math]. In strong induction, however, we assume that a statement is true for all positive integers less than or equal to [math]k[/math].

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