HN Reader

This might be a dumb question but are there any current or foreseeable practical applications of this kind of result (like in the realm of distributed computing) or is this just pure mathematics for its own sake?

First sentence:

> All of modern mathematics is built on the foundation of set theory

That's ignoring most of formalized mathematics, which is progressing rapidly and definitely modern. Lean and Rocq for example are founded on type theory, not set theory.

It's cons'es all the way down.

> All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects

What the hell. What about Type Theory?

> computer science with the finite

um... no... computer science is very concerned with the infinite. I'm surprised quanta published this. I always think highly of their reporting.

Finally - we can calculate infinity.

Been a long way towards it. \o/

One, in theory, can construct number sets (fields) with holes in them - that's truly discrete numbers. such number sets are at most countably infinite, but need not be. One useful such set might have Planck's (length) constant as its smallest number beyond which there is a hole. The problem with using such number sets is that ordinary rules of arithmetic breakdown, ie division has to be defined as modulus Planck constant

Confused why the article author believes this is a surprise. The foundations of mathematics and computer science are basically the same subject (imho) and dualities between representations in both fields have been known for decades.

That’s nothing, ‘node_modules’ has been linking the math of infinity to my filesystem for years.

That’s nothing wait til you see my math.

Emdash all over the article.

It wasn’t just that.. all over the article..

I am getting really strong LLM article vibes.

…that existed in the world of descriptive set theory — about the number of colors required to color certain infinite graphs in a measurable way.

To Bernshteyn, it felt like more than a coincidence. It wasn’t just that computer scientists are like librarians too, shelving problems based on how efficiently their algorithms work. It wasn’t just that these problems could also be written in terms of graphs and colorings. Perhaps, he thought, the two bookshelves had more in common than that. Perhaps the connection between these two fields went much, much deeper. Perhaps all the books, and their shelves, were identical, just written in different languages — and in need of a translator.

When you talk about infinity, you are no longer talking about numbers. Mix it with numbers, you get all sorts of perplexing theories and paradoxes.

The reason is simple - numbers are cuts in the continuum while infinity isn't. It should not even be a symbolic notion of very large number. This is not to say infinity doesn't exist. It doesn't exist as a number and doesn't mix with numbers.

The limits could have been defined saying "as x increases without bound" instead of "as x approaches infinity". There is no target called infinity to approach.

Cantor's stuff can easily be trashed. The very notion of "larger than" belongs to finite numbers. This comparitive notion doesn't apply to concepts that can not be quantified using numbers. Hence one can't say some kind of infinity is larger than the other kinds.

Similarly, his diagonal argument about 1-to-1 mapping can not be extended to infinities, as there is no 1-to-1 mapping that can make sense for those which are not numbers or uniquely identifiable elements. The mapping is broken. No surprise you get weird results and multiple infinities or whatever that came to his mind when he was going through stressful personal situations.

I studied math for a long time. I’m convinced math would be better without infinity. It doesn’t exist. I also think we don’t need numbers too big . But we can leave those