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The way you phrase it suggests that the crime problem is independent of immigration, which is just false. For example, children of two foreign born residents are 5 times more likely to be criminals than children of two native Dutch people. The people have every rational reason to oppose immigration if such a rise in criminality is the outcome.

Ultimately, the problem with deplatforming is not about mere complaining. Students complain all the time about everything. The problem rather is about public disturbance, heckling, and intimidation. That's what the student activists are regularly engaged in.

There's also a second reason why you used the word "campus": because when anyone speaks on a campus, the inanimate campus always hears it. If you said that the "students campuses don't want to hear someone speak", the obvious retort is that nobody is making them do it, they just don't have to attend. Of course, what is actually happening there is not that the majority of students don't want to hear those speakers, instead they don't want the speakers to be able to speak, and they don't want the minority to be able to listen. That's why deplatforming is so pernicious and evil, and why people like to play language games to minimize the illiberalism on campuses.

You are simply illustrating rayiner's point: you don't understand the financial side of running the government, you have no knowledge of actual figures, neither current nor historical, but believe that taxing rich guys even more will solve all the problems we have.

As for police killings, you are comparing an event that’s extremely unlikely to happen with an event that’s multiple orders of magnitude more likely. Speech offense prosecutions in UK are more common today than political prosecutions were in post Kruschev Soviet Union. The only reason UK has fewer political prisoners than Soviet Union had is that the sentences are shorter and typically non-custodial.

If that makes it easier for you to understand it, in the standard proof, you also color every point of the rectangle, with the color of the edge it retracts to (picking the colors of the vertices of the big triangle arbitrarily, just making sure that the color of each vertex is a color of one of the edges it belongs to, not one of the opposite edges). Then, an easy argument from continuity shows that no interior point will have points of three different colors arbitrarily close to it. Finally, applying Sperner's lemma as above proves that such point must nevertheless exist, obtaining contradiction with the existence of the retraction.

and then treated Sperner as an additional ingredient even though the coloring step in Nelson's proof is already the corresponding Sperner argument.

I don't understand what are you saying here. What I'm saying is that for the coloring proof of BFPT to work, whether clothed in standard or nonstandard language, you must perform a combinatorial argument that uses a topology of a triangle as a necessary ingredient, similar in shape to the proof of Sperner's lemma.

In the standard formulation, you apply the Sperner's lemma to find smaller and smaller triangles, and apply compactness, precisely as in the standard proof of intermediate value theorem.

The rest of your post, where you quote reverse mathematics stuff, is completely irrelevant to the point I was making. Nothing I said is about what theorems follows from what axioms, but rather whether nonstandard analysis is meaningfully different, clearer, or more useful language than standard one. It is not.

The language used by mathematicians is subject to constant evolution. 18th and 19th century results in analysis are not expressed and taught in the same way their original authors did it. Newton, Leibniz, Euler, Lagrange, Fourier, Riemann -- none of them expressed their results in terms of epsilons and deltas. These only caught on in the second half of 19th century, and they did so, because they were a better tool to rigorously prove the ideas.

New terminology inventions that make the subjects easier to understand take the field by storm. Some of the relatively recent examples are category theory, homological algebra, or, for that matter, the notion of sheafs, popularized by J.P. Serre himself. Mathematicians are very open to innovation, and intransigence is not the reason why we're stuck with epsilon-delta.

The reason is that nobody has yet come up with a better way of talking about these concepts. I repeatedly observe many people who seem to believe that their difficulty in understanding math stems from mathematicians gatekeeping their results. I think that this belief is just a coping mechanism. Mathematics is genuinely hard, and when people have trouble understanding something, it's easier to think that it's someone else's fault, rather than accepting one's own deficiencies.

There is a certain view, popular among many people, that poor performing schools perform badly because they are underfunded. It has been vigorously spread by politicians, teachers, and activists. Well, we ran the experiment. With enormous federal and state spending, we managed to mostly equalize the spending, and, in many cases, fund the badly performing schools more than the good ones. The results of the experiment are very clear: additional funding, by and large, does not *cause* significantly improved educational outcomes. Any observed correlation between school funding and outcomes is a result of who lives in the area, and who attends the school. The casual arrow does not go from funding to outcomes, but from the school population to both funding, and, in parallel, to outcomes.

And somehow, none of the thousands of very smart mathematicians have done that, or if they had, it has not seen wide adoption. I recommend contemplating on this: if math could be made easier by changing notation, why hasn't this already happened?