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A new bridge links the math of infinity to computer science

254 points by digital55

by md224

1 subcomments

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?

by xjm

4 subcomments

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.

0 subcomment

by anthk

0 subcomment

by shevy-java

5 subcomments

by anon291

4 subcomments

> 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.

by tug2024

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by donw

0 subcomment

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

by alexnewman

14 subcomments

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

by k_bx

6 subcomments

> 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?

by user3939382

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by dboreham

5 subcomments

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.

by FilosofumRex

1 subcomments

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

by zkmon

4 subcomments

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.

by moi2388

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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.