# Frivolous theorem of arithmetic on Wikipedia

1. Apr 9, 2005

### Icebreaker

[SOLVED] Frivolous theorem of arithmetic on Wikipedia

http://en.wikipedia.org/wiki/Frivolous_Theorem_of_Arithmetic

There's a debate on whether we should delete this theorem from Wikipedia because some consider it "useless". Should it be deleted?

2. Apr 9, 2005

### Hurkyl

Staff Emeritus
How does one vote? Just edit the vote for deletion page?

3. Apr 9, 2005

4. Apr 9, 2005

5. Apr 9, 2005

### dextercioby

I think it should be put under a joke-section...

Daniel.

6. Apr 9, 2005

### Icebreaker

But that would raise the question on the "usefulness" of theorems. The way I see it is: if it's true, then it has to be said, no matter how trivial.

7. Apr 9, 2005

### dextercioby

Nope,it is a joke...As for "usefulness" of theorems,i don't see the connections...

Daniel.

8. Apr 9, 2005

### Icebreaker

The entry on wikipedia is being deleted under the pretense that it is not "useful". But then, there are some theorems that are not "useful" which aren't being deleted.

Last edited by a moderator: Apr 9, 2005
9. Apr 9, 2005

### dextercioby

"Useful" is a subjective term.Mathematics is the last place on Earth where u could have subjectivity...

So let's drop it...

Daniel.

10. Apr 9, 2005

### Icebreaker

Which is precisely why the entry should not be deleted under that pretense. But if you feel this way, you can go vote for deletion.

11. Apr 9, 2005

### Hurkyl

Staff Emeritus
Surely you've encountered facts in science that was entirely useless, except that it improved your perspective on things?

12. Apr 9, 2005

### Zurtex

Philistines!

Some people just don't understand the point of mathematics.

13. Apr 9, 2005

### shmoe

I would not call it useless but a humerous reminder of the limitations of finite computations. It happens often enough, piles upon piles of numerical data suggest a function behaves a certain way then it's shown that it does exactly what we expect it not to do outside the range of our fancy computers (e.g. Mertens conjecture).

14. Apr 9, 2005

### hello3719

:rofl: That is the most weak theorem ever, i mean cmon the definitions used are so empty. I bet it isn't a mathematician who suggested that theorem.
( Maybe a physicist, they like to play with "large numbers" :tongue2: )

15. Apr 9, 2005

### Icebreaker

Ah, but it's a theorem nevertheless!

16. Apr 9, 2005

### master_coda

Perhaps wikipedia needs pages describing theorems that tell us that 1+1=2, 1+2=3, 1+3=4, and so on.

17. Apr 9, 2005

### hello3719

yea, it is all about quantity in this world today, who cares about quality!

18. Apr 10, 2005

### Zurtex

And does MathWorld?

http://mathworld.wolfram.com/FrivolousTheoremofArithmetic.html

Oh and please do prove for me rigoursly that 1+1=2, but that's an equation not really a theorem.

You could describe every single number a physicist has ever used as small (I probabily would because I do a lot of cryptography) and still we know that most numbers are large, we have a nice theorem saying so

What has that got to do with this at all?

19. Apr 10, 2005

### arildno

Perhaps Wikipedia needs a section of "The most false theorems" as well:
Here's mine:
The primes are closed under multiplication..

20. Apr 10, 2005

### dextercioby

Zurtex,$1+1=2$ is an equality,not an equation...

Daniel.

21. Apr 10, 2005

### master_coda

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.

22. Apr 10, 2005

### Icebreaker

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?

23. Apr 10, 2005

### shmoe

I've always looked at this frivilous theorem as an amusing (but crude and imprecise) summary of "For every real number M almost all natural numbers are larger than M". 'Almost all' being defined in the usual asymptotic sense-if P(x) is the set of naturals less than x that are larger than M, then P(x) is asymptotic to x as x goes to infinity. I admit I'm easily amused though.

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.

24. Apr 10, 2005

### Hurkyl

Staff Emeritus
There's an interesting interpretation of this theorem in the context of a nonstandard model:

Most natural numbers are external -- here, that means they're bigger than any natural number we can "get" to. (i.e. as long as we stay in the word of natural numbers, doing anything imaginable with internal numbers will never produce an external number)

25. Apr 10, 2005

### Zurtex

Very true, my miswording sorry.