# Tagged Questions

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3answers
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### the following inequality is true，but I can't prove it

The inequality is \begin{equation*} \sum_{k=1}^{2d}\left(1-\frac{1}{2d+2-k}\right)\frac{d^k}{k!}>e^d\left(1-\frac{1}{d}\right) \end{equation*} for all integer $d\geq 1$. I use computer to verify ...
4answers
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### A principle of mathematical induction for partially ordered sets with infima?

Recently I learned that there is a useful analogue of mathematical induction over $\mathbb{R}$ (more precisely, over intervals of the form $[a,\infty)$ or $[a,b]$). It turns out that this is an old ...
10answers
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### Is PA consistent? do we know it?

1) (By Goedel's) One can not prove, in PA, a formula that can be interpreted to express the consistency of PA. (Hopefully I said it right. Specialists correct me, please). 2) There are proofs (...
7answers
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### Unconventional types of induction

Induction is one of the most common tools is mathematics, and everybody knows the ordinary induction and the strong induction. However, in some proofs induction is applied in an unexpected and elegant ...
3answers
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### Easier induction proofs by changing the parameter

When performing induction on say a graph $G=(V,E)$, one has many choices for the induction parameter (e.g. $|V|, |E|$, or $|V|+|E|$). Often, it does not matter what choice one makes because the proof ...
2answers
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### Order statistics (e.g., minimum) of infinite collection of chi-square variates?

Hi everyone, This is my first time here, so please let me know if I can clarify my question in any way (incl. formatting, tags, etc.). (And hopefully I can edit later!) I tried to find references, ...
4answers
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### Examples of “exotic” induction

Next week I am going to teach two lessons on induction to very motivated students from high schools. At some point I would like to talk about ordered sets, well-ordered sets, and mention the fact that ...
1answer
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### Symmetric Proof that Product is Well-Founded

This is a fairly minor, technical question, but I'll toss it out in case someone has a good idea on it. Suppose $(X,<_X)$ and $(Y,<_Y)$ are well-founded orderings (not necessarily linearly ...
2answers
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### Homotopy Transfer Theorem for Differential Graded Associative Algebras

As in Algebra+Homotopy=Operad by Bruno Vallette, let $A$ with multiplication $\nu$ be a differential graded associative algebra equipped with degree +1 map $h$ and let $H$ be a chain complex such that ...
1answer
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1answer
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### notable inductive proofs relating to fractals

what are notable/ prominent inductive proofs relating to fractals? the motivation for this question is: fractals are very difficult mathematical objects to work with, and many problems/questions ...
0answers
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