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Author Topic: Pitagoric Triplet  (Read 11665 times)

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Offline Xeda112358

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Re: Pitagoric Triplet
« Reply #15 on: March 25, 2011, 08:41:38 pm »
:P We discussed this on IRC
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Offline AngelFish

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Re: Pitagoric Triplet
« Reply #16 on: March 25, 2011, 10:20:29 pm »
Does a proof that it's not possible count?
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Offline Munchor

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Re: Pitagoric Triplet
« Reply #17 on: March 26, 2011, 07:14:25 am »
I like what Zeda did, at least, I get most of it :)
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Offline Deep Toaster

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Re: Pitagoric Triplet
« Reply #18 on: March 26, 2011, 01:26:33 pm »
Quote from: Qwerty.55 on March 25, 2011, 10:20:29 pm
Does a proof that it's not possible count?

Sure. Post a full, formal proof here.
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Offline Goplat

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Re: Pitagoric Triplet
« Reply #19 on: March 26, 2011, 07:07:35 pm »
Quote from: Deep Thought on March 25, 2011, 08:41:09 pm
Here's a harder one: Find natural numbers a, b, and c where a3+b3=c3 :P

03 + 03 = 03

And yes, 0 is a natural number. The standard way to define the natural numbers in modern mathematics is to represent 0 with the empty set, 1 as the set {0}, 2 as the set {0,1}, etc.
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Offline AngelFish

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Re: Pitagoric Triplet
« Reply #20 on: March 26, 2011, 07:25:12 pm »
That's defining the cardinality as a number, which it does not appear to be. For example, the cardinality of the set of natural numbers is infinity. The cardinality of the set of real numbers is of a greater infinity. If cardinality are real numbers, then would there not be multiple types of natural infinities?
« Last Edit: March 26, 2011, 07:25:34 pm by Qwerty.55 »
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∂²Ψ    -(2m(V(x)-E)Ψ
---  = -------------
∂x²        ℏ²Ψ
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