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1 1 Why do we need proof by induction? A natural starting point for proving many mathematical results is to look at a few simple

The principle of mathematical induction can be used to prove a wide range of statements involving variables that take discrete values Some typical examples are

To prove something by mathematical induction you first do the base case, to show that the statement holds for the smallest integer Then you do the induc- tion

To do so, simply plug n = 0 into the original equation and verify that if you add all the integers from 0 to 0, you get 0(0+1)/2 Sometimes you need to prove

The method of mathematical induction for proving results is very important in the study of Stochastic Processes This is because a stochastic process builds up

Proof by Induction ? Suppose that you want to prove that some property P(n) holds of all natural numbers To do so: ? Prove that P(0) is true

Proof by Induction ? Suppose that you want to prove that some property P(n) holds of all natural numbers To do so: ? Prove that P(0) is true

Math 213 Worksheet: Induction Proofs A J Hildebrand Begin any induction proof by stating precisely, and prominently, the statement (“P(n)”) you plan

(b) From part (a), make a conjecture as to the value of an for any positive integer n (c) Use the principle of mathematical induction to prove that your

To make this simple mathematical example, we could write: To understand the basic principles of mathematical induction, suppose a set of thin

n can be any positive integer 1 1 Why do we need proof by induction? A natural starting point for proving many mathematical results is to look at a few simple

The principle of mathematical induction may be stated as follows: Suppose the following can be proved about a statement or proposition, , about positive integers:

The idea of mathematical induction Basic induction proofs (e g equality, inequality, property,etc) An interesting Induction step: assume can tile 2n x 2n,

Mathematical induction is a finite proof pattern for proving propositions of the form n N P( n ) With mathematical induction, a “theory” can be proved

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