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top ten coolest numbers

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I think that the coolest number is the first uncool number :)

I completely agree with your choice of making 2 apear in your list. It has been said many times that "2 is a very odd prime".

Another reason you may want to add to your endorsement for 2 is that x^p+y^p=z^p has solutions for p=2 but not for any other prime! (i.e. FLT). This is actually quite surprising and singles out the prime 2.

Alvaro

Excellent point. I'll add that immediately.

Cam

Because 1+2+3=1.2.3 and there is not another one with that property!

In fact we could say that the first uncool number is 0 because I cannot divide any number (except, possibly, the same one)by him. What a subjectiveness!

However, 4 is cooler:

4 = 2 + 2 = 2*2 = 2^2... and it's the only one with THAT property.
--
"It's John Ashcroft's vision of hell. It's a Tom Waits song."
Simon - mhm27x5

Why not? That's your opinion. I like the six because 1,2,3 are the proper divisors of 6. And that's the point about the mathematical context of ``cool number''. I think that mathcam entry has to do with curious/notable numbers. However rspuzio, apparently, through 'paradox' tries to give a logical/mathematical sense to the mentioned phrase (or it just was a joke?).

I think that the first uncool number is the last uncool number... Let's find it...
Is this math?

6 is unique also being the least order giving a non-commutative group =o)

4 is unique also in having the property that the least non-commutative ring, the "Klein 4-ring", consists of four elements =o)

A_4 is also the only non-simple alternating group.

4 is also unique in that R^n has a unique differentiable structure for all n... except 4.
--
"It's John Ashcroft's vision of hell. It's a Tom Waits song."
Simon - mhm27x5

> 4 is also unique in that R^n has a unique differentiable
> structure for all n... except 4.

Is that right? I thought it was just the smallest n with that property. I actually thought about putting 4 on the list because of that, but if it's *unique* in having that property, it might at least earn 4 an honorable mention.

Cam

I'm pretty sure it's unique... at least every time I've heard that mentioned, it's always been said that way.

If that is the case though, it (at least to me) puts 4 in a pretty special category. All the other little things I mentioned are curiosities (and the A_4 bit is, admittedly, somewhat artificial)... but the differentiable structure thing... that's interesting.
--
"It's John Ashcroft's vision of hell. It's a Tom Waits song."
Simon

...the "Ten Coolest Numbers" article just got Dugg.

The ensuing discussion is rather humorous.

http://digg.com/general_sciences/The_Ten_Coolest_Numbers

Cam

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