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 Mar 6 revised For which coverings by “geometrically nice” sets does the nerve admit “Vietoris-Rips-like” approximations? Language Mar 6 asked For which coverings by “geometrically nice” sets does the nerve admit “Vietoris-Rips-like” approximations? Jun 21 comment $\int f(x) dx$ is appearing as $\int dx f(x)$. Why? One "justification" I've heard is that if you consider integration as a function taking, say, integrable functions to real number, then writing $\int \mathrm{d}x f$ sort of looks like "applying the function $\int \mathrm{d}x$ to $f$". I don't like the argument myself, but it's one I've heard at least. Jun 21 comment $\int f(x) dx$ is appearing as $\int dx f(x)$. Why? It's just notation. Jun 20 awarded Critic Jun 19 comment What is the usefulness of matrices? Also, if the teacher who couldn't answer your question is the same one who is teaching you about matrices, I would be very skeptical of her and the course. Jun 19 comment What is the usefulness of matrices? A matrix is a way to express a linear map between finite-dimensional vector spaces, given a choice of bases for said spaces. Since linear maps are useful, matrices are obviously useful. May 21 awarded Editor May 21 revised Locally closed subspaces and sheaves. Missing restriction in final formula. May 21 awarded Teacher May 18 answered Locally closed subspaces and sheaves. May 18 awarded Commentator May 18 awarded Citizen Patrol May 16 comment Pullback of a locally constant sheaf by a function whose domain is simply connected No, no problem. I realized my comment was nonsensical. Everything you say is essentially direct. May 16 awarded Scholar May 16 accepted Pullback of a locally constant sheaf by a function whose domain is simply connected May 16 awarded Student May 16 asked Pullback of a locally constant sheaf by a function whose domain is simply connected Apr 18 comment Is there a way of defining the notion of a variable mathematically? The word "variable" means many different things, and many of these meanings are non-rigorous. What do you mean by "variable"? Apr 12 comment Improving my understanding of Cantor's Diagonal Argument @MooingDuck: I hope I'm not turning this into a chat, but regarding the second question, one thing (probably already pointed out) springs to mind: What do you mean by "the last element" in this infinite sequence?