# Tagged Questions

Questions asking for a "big list" of examples, illustrations, etc. Ask only when the topic is compelling, and please do not use this as the only tag for a question.

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### Good true-false linear algebra questions?

Can you suggest me a collection of true-false linear algebra questions, like the ones found in the MIT exams, if possible with solutions (i.e. explanations)? Sorry if it turns out that my request is ...
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### Can one extend the analogy between mathematics and art beyond a just “pleasing” result? [on hold]

This is a soft question. It's extremely commonplace for mathematician's to refer to work as "elegant," "beautiful," and I've seen many compare the process of doing mathematics to painting, or playing ...
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### Continuous functions with orbit of period $3$

I would like to build some continuous functions $f : E \to \Bbb R$ (where $E \subset \Bbb R$ is an interval), such that $$\exists x \in E,\;\; [f(x)≠x≠f(f(x)),\;\; f^3(x):= f(f(f(x)))=x]$$ I tried ...
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### In which topologies do open sets maintain open under countable or arbitrary intersection?

We know that in the usual topology, countable or arbitrary intersection of open sets can zoom into a singleton, hence is not in the topology. I am curious if there is well known classes of ...
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### Proving convergence or divergence of series: Tips and Tricks

I currently write an article where I collect some tips for students for proving the convergence or divergence of series. What tips and tricks do you know or use or teach? Remark: I will add some ...
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### Seeking advice from the more experienced on which trig identities are crucial to memorize and which can be derived quickly

This is a bit of a two part question. I also have read some of the related questions, but I think mine is different as whether they can be derived quickly, rather than whether they can be derived, is ...
3k views

### Big List of Erdős' elementary proofs

Paul Erdős was one of the greatest mathematicians of all time and he was famous for his elegant proofs from The Book. I posted a question about one of his theorem and got a reference, and I have other ...
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### Noteworthy examples of finite categories

So far all the finite categories I have encountered fall into one of these c̶a̶t̶e̶g̶o̶r̶i̶e̶s̶ sets: finite monoids finite preorders just formal devices to explain, what a "diagram" in another (...
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### What are the most obscure or advanced mathematics with practical application

Throughout my engineering studies there were jokes made by my professors (mostly mathematics professors) that referenced the fact that pure mathematicians strive to create mathematics with no ...
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### What properties of the real numbers are almost always true and there are no (or very few) known examples of?

What properties of the positive real numbers are almost always true and there are no (or very few) known examples of? Two that come to mind are numbers that are normal in every base and numbers ...
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The Problem Show that the number of possible links in a computer network of $n$ computers ($n \in Z \land n \geq 1$) is $\frac{n(n-1)}{2}$ in as many ways as you can. My Work Solution 1 Given $n$ ...
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### Problem sets on Abstract Algebra

Many times we ask about what books should we read to learn or know more about a math topic (Abstract Algebra, in this case). However, I would like to get a list of the exercises what should we solve ...
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### What are some interesting results that could be derived if some conjectures were true/false?

I recently came up on Djikstra's idea of a fictional company called Mathematics.Inc which produced proofs as trade secrets which could then be used by customers.. For example, it produced the proof of ...
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### Exceptions in infinite-dimensional spaces

What are the properties that are true in finite-dimensional spaces but fails in the infinite-dimensional space? For example, the closed unit ball is compact only in finite-dimensional normed space.
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### When adding zero really counts …

Note: Although adding zero has usually no effect, there is sometimes a situation where it is the essence of a calculation which drives the development into a surprisingly fruitful direction. Here is ...
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### Curvature and topology

I am studying Riemannian Geometry and I came across various Theorems which give conditions on the topology of a manifold given conditions on curvature, and vice-versa. Just to mention a few of them: ...
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### Books with SAGE portions

I recently finished working through Adventures in Group Theory and really appreciated the use of SageMath it employs. I considered myself moderately proficient with Sage, but I found working through ...