# Frivolous theorem of arithmetic on Wikipedia

Icebreaker said:
The page can be updated, modified; information can be added. Why don't you go add something to the page instead of deleting it altogether?
Because I don't care about this theorem enough to spend time trying to produce a worthwhile article about it. Of course, I haven't deleted it either; I just think it should be deleted, since the current article is nothing but noise. It should be up to the people who actually think the theorem is interesting to produce good content describing it.

shmoe said:
This is definitely true. A more precise statement, especially how we would try to quantify 'very large' and 'almost all', would be ideal in the currently non-existant body of the article as well as an explanation of practical implications. I'm not sure if there's any interesting folklore behind this, but if there is it would be a nice addition as well.
I don't think there's anything wrong with the fact that this isn't a "real theorem" (although a more mathematical restatement of it would be ideal). I just thought it was strange that someone would tell me that 1+1=2 isn't a theorem in defence of something else which is very clearly not a theorem.

Last edited:
Zurtex
Homework Helper
master_coda said:
1+1=2 is much more of a theorem that the frivolous one being discussed. It's a provably true mathematical statement. "Almost all natural numbers are very, very, very large" is not a mathematical statement, and so it certainly isn't a real theorem.

But the real problem with the page is not that the theorem is useless, it's that the page is. The page provides no useful information at all; it doesn't explain why the theorem is true or what its significance is. If you already know the theorem then the page doesn't tell you anything new or interesting. And if you don't know the theorem then you aren't going to learn anything from the useless remarks on the page.
I didn't realise there was scale of theromness, please tell us how this scale works so I know how to order my theorems from now on in their level theoremality. I would certainly like to know which theorems are more of theorems than your average theorem.

I found the equivalent MathWorld page quite enlightening when I came across it.

Zurtex said:
I found the equivalent MathWorld page quite enlightening when I came across it.
What new insight into mathematics (or anything else) did you get from finding this theorem?

Icebreaker
Are you implying that the theorem is not useful?

Hurkyl
Staff Emeritus
Gold Member
I put this theorem into the class of things everybody knows, but few actually realize until they have it pointed out to them. There are lots of such facts... for instance, once I saw the example of a nonzero function whose taylor series was zero, it took me several years before it dawned on me that most infinitely differentiable functions are not analytic. :yuck: But, if at any point, someone had stated that fact to me, my reaction would've been "Oh right, that's obvious!"

Icebreaker said:
Are you implying that the theorem is not useful?
No, I think the page is not useful. It could probably be made useful by adding more content. But all it has right now is filler. For example, the "one of the more interesting theorems of mathematics" comment could be replaced by text that actually explains why the theorem is supposed to be interesting.

Zurtex