A recent spate of vague questions under the tag philosophy suggests that it may be worth clarifying the purpose of the tag by ruling out a certain type of questions explicitly. These are questions that offer "vague philosophizing" rather than posing a question in the philosophy of mathematics. Su...

The set-theory tag is explicitly about mathematics (and metamathematics) in the context of $\mathsf{ZFC}$ and its subsystems and extensions. Every now and then we see questions about other set theories ($\mathsf{NF}$ is popular enough, but there are other versions, see here, for instance). ...

The infinite group in which every element has infinitely many square roots and every element is of order $2^n$. What do we know about this group? Are there any well-studied constructions of it? If it even exists. i.e. there are infinitely many $a_1$ such that $a_1\cdot a_1=1$ and further,...

At the moment we have two tags transfinite-induction and transfinite-recursion. These topics are rather close. I can imagine a reasonable question which could be tagged with the tags transfinite-induction, transfinite-recursion, ordinals, elementary-set-theory. Having only five spots for tags, t...

If I want to compute the shortest path between two points in a directed graph, I can use the Dijkistra algorithm. But what if I want to compute the longest path? If the weights on the graph are bounded, then I guess I can use Djkstra to the graph with weights $M-c_i$, where $M = \max_i c_i$. Is...

Suppose $(X,d)$ is a metric space with the nearest point property and $a,b \in X$ with $a \ne b$. Suppose there is a path of finite length in $X$ from $a$ to $b$ and let $m$ be the infimum of the lengths of all paths from $a$ to $b$.Then, by Lipschitz reparametrization, there exists a path $g:[0...

I'm looking for a way to, in any given connected, undirected graph, calculate a path between any two nodes with a cost as close as possible to a given value. The example is in this image (sorry, I can't embed images yet): A simple graph Note: the visual length of each edge doesn't exactly ma...

Given this question, what about the special case when the start point and end point are the same? I ask it here instead because I am looking for the mathematical solution to counting these different paths. Another change in my case is that we must move at every step. How many such different path...