Post a number with an interesting property

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marshall
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25 Oct 2015, 10:24 pm

Rudin wrote:

marshall wrote:

Apparently the Feigenbaum constant hasn't yet been proven to be transcendental (though it most likely is). Also, no closed form representation involving other known transcendental numbers has been found. Nor has a closed form infinite series been found.

I don't think it has even been proved to be transcendental.

It hasn't. I already corrected myself

It's likely transcendental, but we won't know for sure until someone comes up with a proof.

Rudin
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26 Oct 2015, 6:36 am

marshall wrote:

Rudin wrote:

marshall wrote:

I don't think it has even been proved to be transcendental.

It hasn't. I already corrected myself

It's likely transcendental, but we won't know for sure until someone comes up with a proof.

Bollocks! Sorry, I meant irrational not transcendental.

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Rudin
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01 Nov 2015, 7:55 am

China's constant is a really awesome number.

Rudin
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06 Nov 2015, 11:29 am

1 is a really cool number.

It can be expressed as cubes of three integers in infinitely many ways. That's just one of the cool things about it.

naturalplastic
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06 Nov 2015, 4:58 pm

Rudin wrote:

1 is a really cool number.

It can be expressed as cubes of three integers in infinitely many ways. That's just one of the cool things about it.

Huh?

Are you saying that the number one has three different cube roots?

Rudin
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06 Nov 2015, 5:16 pm

naturalplastic wrote:

Rudin wrote:

1 is a really cool number.

It can be expressed as cubes of three integers in infinitely many ways. That's just one of the cool things about it.

Huh?

Are you saying that the number one has three different cube roots?

I mean the sum of three cubes in infinitely many ways.

nurseangela
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06 Nov 2015, 5:24 pm

My favorite number - 8. It has no beginning and it has no end and if you put it on its side it goes for "infinity".

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naturalplastic
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06 Nov 2015, 5:49 pm

Rudin wrote:

naturalplastic wrote:

Rudin wrote:

1 is a really cool number.

It can be expressed as cubes of three integers in infinitely many ways. That's just one of the cool things about it.

Huh?

Are you saying that the number one has three different cube roots?

I mean the sum of three cubes in infinitely many ways.

You still aren't conveying what the heck you're talking about.
The sum of the cubes of three positive integers above one?
Is that what you mean?

The sum of the cubes of the three smallest positive integers above one is not anything like one.

naturalplastic
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06 Nov 2015, 6:06 pm

nurseangela wrote:

My favorite number - 8. It has no beginning and it has no end and if you put it on its side it goes for "infinity".

Eight has a sexy hourglass figure!

Actually eight IS an hourglass "figure".

Nine is the first odd number that is NOT a prime number. And two is the only even number that is prime.

Rudin
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06 Nov 2015, 8:58 pm

naturalplastic wrote:

Rudin wrote:

naturalplastic wrote:

Rudin wrote:

1 is a really cool number.

It can be expressed as cubes of three integers in infinitely many ways. That's just one of the cool things about it.

Huh?

Are you saying that the number one has three different cube roots?

I mean the sum of three cubes in infinitely many ways.

There are infinitely many integers a,b,c such that a^3+b^3+c^3=1.

naturalplastic
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06 Nov 2015, 11:51 pm

Rudin wrote:

naturalplastic wrote:

Rudin wrote:

naturalplastic wrote:

Rudin wrote:

1 is a really cool number.

It can be expressed as cubes of three integers in infinitely many ways. That's just one of the cool things about it.

Huh?

Are you saying that the number one has three different cube roots?

I mean the sum of three cubes in infinitely many ways.

There are infinitely many integers a,b,c such that a^3+b^3+c^3=1.

A) Can't you take a hint? I am obviously asking you for examples. Would it kill ya to give me an example of three integers that add up that way?

B) I asked above if you were including negative integers, or not. You didnt answer my question.

C) Even if you ARE including negative integers its hard for a non mathematician like me to think of an example of a combination of three integers (any mix of negative and or positive) that add up that way.

D) If you could get three cubed integers to add up to one, then wouldnt you also be able to find combinations that would add up to ANY integer? Wouldnt this be a characteristic of every integer? If so then what would this have to do with making the number one "special"?

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07 Nov 2015, 8:56 am

I said integers, so of course they can be negative (and 0). If they couldn't be negative I would specify.

1=(1+9n^3)^3+(9n^4)^3+(-9n^4-3n)^3

You can plug in any n you'd like. For instance,

1=1^3+0^3+0^3

And,

1=10^3+9^3-(12)^3

One is the only number that has been proven to have this property. You could expand out the parametric solution above and add it all up and you'd get one by the way.

naturalplastic
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07 Nov 2015, 9:52 am

Okay.

SippingSpiderVenom
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07 Nov 2015, 2:18 pm

There are infinitely many integers a,b,c such that:

a^3+b^3+c^3=1

Ex:
10^3+9^3+(-12)^3=1

looks closer to:
(±a)^3+(±b)^3+(±c)^3=1
where a, b, & c are infinite integers and at least one variable is the opposite sign of the other two.

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08 Nov 2015, 10:44 am

Well you could also have,

1=1^3+x^3+(-x)^3

That's much easier to prove.

SippingSpiderVenom
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08 Nov 2015, 3:22 pm

Well that's better, but zero would also have that property and it doesn't hold that a^3+b^3+(-c)^3=1 unless b=c.

How did you find a=10, b=9, & c=-12?

~ssv

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