# A (tongue-in-cheek) proposal that the set of natural numbers is finite?

September 8, 2019 1:24 PM Subscribe

A while back I read a fascinating paper by a real mathematician (read: not a crank) who made the claim that the set of natural numbers is in fact finite. It was an entertaining read, but somehow I didn't bookmark it and I haven't been able to turn it up again. I'm hoping someone else at MeFi knows of it.

Here's what I remember: The main thrust of the thing was that the set of natural numbers is essentially a finite group, so it basically 'wraps around' from some unfathomably large number back to zero. A consequence was that there becomes a smallest rational number, and I think the author spent some time talking about the consequences of this for calculus.

The author had a great sense of humor about the whole thing, presenting himself with a wink.

Biographically, I am pretty sure I did some cursory googling on the author and found that it was an older male professor at a reputable institution.

I am also pretty sure I found the article after going down a rabbit hole learning about 'intuitionism', after I discovered there are people who don't accept the law of the excluded middle EVER (i.e., if x is not greater than y, and x is not less than y, they would dispute that x must be equal to y, in general, even in an ordered set). I did a bunch of internet reading on it, which kind of culminated in this paper.

The bonus here is that if you are able to find what I'm talking about, and haven't read it before, then you're in for a treat!

Here's what I remember: The main thrust of the thing was that the set of natural numbers is essentially a finite group, so it basically 'wraps around' from some unfathomably large number back to zero. A consequence was that there becomes a smallest rational number, and I think the author spent some time talking about the consequences of this for calculus.

The author had a great sense of humor about the whole thing, presenting himself with a wink.

Biographically, I am pretty sure I did some cursory googling on the author and found that it was an older male professor at a reputable institution.

I am also pretty sure I found the article after going down a rabbit hole learning about 'intuitionism', after I discovered there are people who don't accept the law of the excluded middle EVER (i.e., if x is not greater than y, and x is not less than y, they would dispute that x must be equal to y, in general, even in an ordered set). I did a bunch of internet reading on it, which kind of culminated in this paper.

The bonus here is that if you are able to find what I'm talking about, and haven't read it before, then you're in for a treat!

That's it for sure. Thanks so much!!

posted by dbx at 2:17 PM on September 8, 2019 [1 favorite]

posted by dbx at 2:17 PM on September 8, 2019 [1 favorite]

Ha, wow that’s something! Thanks for asking/informing me of this.

I’ll never forget the face my (semi-famous) professor of abstract algebra made when he told us some otherwise-reputable sources chose to reject the law of the excluded middle!

Really, once you acknowledge the empty set and the concept of set inclusion, a lot of our reasonable intuitions go to hell ;)

posted by SaltySalticid at 5:22 PM on September 8, 2019

I’ll never forget the face my (semi-famous) professor of abstract algebra made when he told us some otherwise-reputable sources chose to reject the law of the excluded middle!

Really, once you acknowledge the empty set and the concept of set inclusion, a lot of our reasonable intuitions go to hell ;)

posted by SaltySalticid at 5:22 PM on September 8, 2019

This was wonderful, by the way-- thanks for asking because I have now

posted by peppercorn at 11:08 PM on September 8, 2019

*totally*fallen down an ultrafinite rabbit hole :)posted by peppercorn at 11:08 PM on September 8, 2019

You are not logged in, either login or create an account to post comments

posted by J.K. Seazer at 2:04 PM on September 8, 2019 [10 favorites]