# Tagged Questions

108 views

### Most unusual form of mathematical induction

After reading the algebraic proof of Fundamental Theorem of Algebra, where induction was carried out on "The highest power of $2$ dividing $n$", which I regard to be unusual and brilliant at the same ...
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### What is the first proof that you've done using induction?

Right now in class I'm learning induction and I'm having a hard time to grasp the concepts of it, especially strong induction which confuses me even further. But out of curiosity, what is the first ...
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### Equality such that induction step is valid but basis is not?

I always puzzled why the two steps are so different in complexity: almost for any proof checking the basis assertion is simple mechanical procedure, while most of the work deferred to proving ...
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### Examples of mathematical induction

What are the best examples of mathematical induction available at the secondary-school level---totally elementary---that do not involve expressions of the form $\bullet+\cdots\cdots\cdots+\bullet$ ...
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### Must we use induction to prove a statement for all integers

This question is prompted by a remark from Bill Dubuque in his answer to this question on proving a particular sum without using mathematical induction. From Bill's answer: A proof that a ...
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### Infinite induction “valid”

As you may know, induction works only when we have a statement involving natural numbers. For instance, For every $n$, the intersection of $n$ open sets is open. Now, the corresponding statement for ...
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### A resource of exercises about induction and combinatorics

I'm looking for a book, webpage or similar resource with a lot of exercises about induction and combinatorics at basic level.