Discrete math : Induction proof

Thread starter boxz
Start date Sep 20, 2013
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Discrete Discrete math Induction Proof

In summary, discrete math is a branch of mathematics that deals with countable, finite, or distinct objects and their relationships. Induction proof is a mathematical method used to prove statements or theorems for all natural numbers, involving a base case and an inductive step. The purpose of using induction proof is to show that a statement is true for all natural numbers efficiently. The steps involved in an induction proof are proving a base case, assuming an inductive hypothesis, using the hypothesis in the inductive step, and concluding using the principle of mathematical induction. Some common mistakes to avoid in induction proofs include using the wrong base case, not using the inductive hypothesis correctly, assuming without proof, and not clearly stating the conclusion or using the principle

Sep 20, 2013

boxz

Stuck on the induction step,please help

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Sep 20, 2013

szynkasz

For ##n+1## you get one extra number. If it is even you can add it to the "even" sets you have for ##n## and you get additional sets. Count them.

What is discrete math?

Discrete math is a branch of mathematics that deals with countable, finite, or distinct objects and their relationships. It includes topics such as set theory, combinatorics, and graph theory.

What is induction proof?

Induction proof is a mathematical method used to prove statements or theorems for all natural numbers. It involves proving a base case and then showing that if the statement holds for a particular number, it also holds for the next number.

What is the purpose of using induction proof?

The purpose of using induction proof is to show that a statement or theorem is true for all natural numbers, without having to prove it for each individual number. It allows for a more efficient and general proof.

What are the steps involved in an induction proof?

The steps involved in an induction proof are:

Base case: Prove that the statement holds for the first natural number (usually 0 or 1).
Inductive hypothesis: Assume that the statement holds for some arbitrary natural number, k.
Inductive step: Use the inductive hypothesis to show that the statement also holds for the next natural number, k+1.
Conclusion: Conclude that the statement holds for all natural numbers by the principle of mathematical induction.

What are some common mistakes to avoid in induction proofs?

Some common mistakes to avoid in induction proofs include:

Using the wrong base case or assuming the statement holds for a different number than the one given.
Skipping the inductive hypothesis or not using it correctly in the inductive step.
Assuming that the statement holds for all natural numbers without actually proving it.
Not clearly stating the conclusion or not using the principle of mathematical induction to conclude.