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@giuseppebilotta@fediscience.org it is best looked at with an example, as close to your problem as possible, perhaps even with a software package in hand. In this case the Wikipedia article is not that good. In actual fact, you may find that this is a good use case for an LLM. Linear programming is common enough that it's very prevalent in training data, and you'll be able to check any hallucinations. I'd simplify your problem as much as possible, state it, and ask it to transform that into the standard form of a linear program. If in fact your problem doesn't fit, it may even tell you. If you do, share your results. I'd be interested to know whether it is useful or not...

@giuseppebilotta@fediscience.org this is linear programming. If you solve your initial linear problem (expressible in matrix form as Ax = b) as far as possible, you end up with a linear space of solutions with some dimension n (less than the number of variables you started with, but more than zero, because it's underdetermined). You want to consider only solutions x where you minimize some linear function of x, and also put linear conditions on x. This turns it into a classic linear programming problem. There are very effective software packages for solving linear programming problems, but you generally have to massage your problem into a standard form, which can take some doing if you're not familiar with this.

@funkylab @pustam_egr @lowrankjack and collections of open sets are not the same as topological spaces but seem to be labelled the same.

@abuseofnotation@mathstodon.xyz I think the advantage of set theory is that, although it is abstract, the notion is extremely basic and obvious in a way that doesn't apply to categories. Types are also fairly obvious, at least for programmers. The need to develop it axiomatically causes some complication, but the nice thing is that the axioms are not, in practice, limiting. Set theorists did the work of showing that all normal mathematical objects can be formalised as sets, and then the Separation Scheme gives non-set-theorists exactly what you had in Naïve Set Theory.