Frivolous theorem of arithmetic on Wikipedia

In summary, there is a debate on whether the Frivolous Theorem of Arithmetic should be deleted from Wikipedia due to its perceived uselessness. Some argue that it should be kept under a joke section, while others believe that if it is true, it should be included regardless of its trivial nature. The discussion has also brought up the subjectivity of the term "useful" in mathematics. However, the main issue with the current Wikipedia page is that it lacks any useful information or explanation of the theorem's significance. Some have suggested updating and modifying the page, but others feel it is not worth the effort.
  • #1
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?
 
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  • #2
How does one vote? Just edit the vote for deletion page?
 
  • #5
I think it should be put under a joke-section...

Daniel.
 
  • #6
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
Nope,it is a joke...As for "usefulness" of theorems,i don't see the connections...

Daniel.
 
  • #8
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.
 
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  • #9
"Useful" is a subjective term.Mathematics is the last place on Earth where u could have subjectivity...

So let's drop it...

Daniel.
 
  • #10
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
Surely you've encountered facts in science that was entirely useless, except that it improved your perspective on things?
 
  • #12
Philistines!

Some people just don't understand the point of mathematics.
 
  • #13
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
:smile: 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" :-p )
 
  • #15
Ah, but it's a theorem nevertheless!
 
  • #16
Perhaps wikipedia needs pages describing theorems that tell us that 1+1=2, 1+2=3, 1+3=4, and so on.
 
  • #17
yea, it is all about quantity in this world today, who cares about quality!
 
  • #18
master_coda said:
Perhaps wikipedia needs pages describing theorems that tell us that 1+1=2, 1+2=3, 1+3=4, and so on.
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.

hello3719 said:
:smile: 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" :-p )
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 :approve:

hello3719 said:
yea, it is all about quantity in this world today, who cares about quality!
What has that got to do with this at all?
 
  • #19
Perhaps Wikipedia needs a section of "The most false theorems" as well:
Here's mine:
The primes are closed under multiplication..
 
  • #20
Zurtex,[itex] 1+1=2 [/itex] is an equality,not an equation...


Daniel.
 
  • #21
Zurtex said:
Oh and please do prove for me rigoursly that 1+1=2, but that's an equation not really a theorem.

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
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
master_coda said:
"Almost all natural numbers are very, very, very large" is not a mathematical statement, and so it certainly isn't a real theorem.

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.

master_coda said:
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.

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
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
dextercioby said:
Zurtex,[itex] 1+1=2 [/itex] is an equality,not an equation...


Daniel.
Very true, my miswording sorry.
 
  • #26
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.
 
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  • #27
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 realize 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.
 
  • #28
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?
 
  • #29
Are you implying that the theorem is not useful?
 
  • #30
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. But, if at any point, someone had stated that fact to me, my reaction would've been "Oh right, that's obvious!"
 
  • #31
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.
 
  • #32
Yeah yeah I know, some times I take things too seriously, I've edited the front page, please edit anything I've wrote if you can think of something better.
 
  • #33
I remember it being proven by someone "jokingly" a while back on one of the threads. That proof is much more simple, iirc.
 

Related to Frivolous theorem of arithmetic on Wikipedia

1. What is the frivolous theorem of arithmetic?

The frivolous theorem of arithmetic is a mathematical statement that states that every positive integer is equal to the sum of its divisors. This theorem is considered "frivolous" because it is trivially true and does not provide any new or useful information.

2. Who discovered the frivolous theorem of arithmetic?

The frivolous theorem of arithmetic was first stated by the mathematician Paul Erdős in the 1930s. However, it was known to mathematicians long before Erdős, and it has been referenced in various forms since the 18th century.

3. Is the frivolous theorem of arithmetic useful?

No, the frivolous theorem of arithmetic is not considered useful in the field of mathematics. It is often used as an example of a trivial or obvious statement.

4. What is the significance of the term "frivolous" in this theorem?

The term "frivolous" in the frivolous theorem of arithmetic refers to the fact that the statement is trivially true and does not provide any new or interesting information. It is considered a joke among mathematicians and is often used as an example of a useless theorem.

5. Are there any real-world applications of the frivolous theorem of arithmetic?

No, there are no known real-world applications of the frivolous theorem of arithmetic. It is purely a mathematical curiosity and has no practical use.

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