# Tag Info

Accepted

### Does a proof by induction have to explicitly refer to the principle of mathematical induction?

The appropriate level of granularity for a proof depends on the audience. If you're taking an "Intro to Proofs" class and your homework is to do some proofs by induction, then yeah, you ...
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### Good, simple examples of induction?

Here is another one: $\color{blue}{\text{Prove that the power of$13$can be writen as a sum of two squares}}.$ I will give two proofs of it. First one is more involved and includes the following ...
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### Does induction really avoid proving an infinite number of claims?

The "avoidance of proving an infinite number of claims" explanation for the need for induction has not yet resonated with me because there are obviously many universally quantified ...
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### Does induction really avoid proving an infinite number of claims?

My personal take on this, is that all the talk about "infinite this, and infinite that" is only mudding the waters. The emphasis should not be on wanting to prove $P(n)$ for all all $n$, but ...
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### Why are induction proofs so challenging for students?

As already touched on here, perhaps proof by induction should not be the first real method of proof that students learn. (The two-column proofs of geometry common in North American schools don't ...
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### Does induction really avoid proving an infinite number of claims?

The statement Since we can't go over "manually proving" all claims 1,2,… and actually get to the finish line in a finite time, we use induction to prove "all the claims at once". ...

### 'Low-algebra' examples of induction

Tiling problems might meet your constraints. A nice simple example is Golomb's Theorem that a chessboard of side $2^n$ with any square omitted can be tiled by trominoes ("L" shapes of 3 squares). In ...
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Accepted

### Is induction or recursion easier to understand?

One thing that you have to keep in mind here, is that you don't need to understand recursion to implement it. There is a big difference between "we were taught to do it like that, I implement it and ...
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### Does a proof by induction have to explicitly refer to the principle of mathematical induction?

A blast from the past comment, for the consolation of your students, of a mathematician being marked down by one of the most influential mathematicians of his day: John Wallis in his Arithmetica ...
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### Good, simple examples of induction?

For what natural $n$ does there exist a square composed of $n$ squares? Example: 1, 4, and 6 are valid, but one cannot construct a square from 2, 3, or 5 squares. Proof:
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### Does a proof by induction have to explicitly refer to the principle of mathematical induction?

I am (one of the) colleagues David refers to in his post. The reason I am doing this lies in some of the answers/comments posted here already. For example, Humberto sais: "While technically it ...
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