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Current time: 23rd June 2017, 23:45

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The Mathematical Proof Thread
#11
RE: The Mathematical Proof Thread
I proved Goldbach's Conjecture last week while I was making tea. I wrote the proof on a napkin, but my dog ate it. Sorry.

Boru
'There are people who long for immortality in the afterlife who don't know what to do with themselves on a rainy Sunday afternoon.' - Isaac Asimov
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#12
RE: The Mathematical Proof Thread
(14th September 2016, 04:04)BrianSoddingBoru4 Wrote: I proved Goldbach's Conjecture last week while I was making tea.  I wrote the proof on a napkin, but my dog ate it.  Sorry.

Boru

Would you believe that that exact same thing happened to me with my theory of everything? What are the odds!
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition

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#13
RE: The Mathematical Proof Thread
(14th September 2016, 04:06)Alex K Wrote:
(14th September 2016, 04:04)BrianSoddingBoru4 Wrote: I proved Goldbach's Conjecture last week while I was making tea.  I wrote the proof on a napkin, but my dog ate it.  Sorry.

Boru

Would you believe that that exact same thing happened to me with my theory of everything? What are the odds!


Cleary, the odds are 1:1. I assert this, can't prove it.

Boru
'There are people who long for immortality in the afterlife who don't know what to do with themselves on a rainy Sunday afternoon.' - Isaac Asimov
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#14
RE: The Mathematical Proof Thread
(14th September 2016, 04:08)BrianSoddingBoru4 Wrote:
(14th September 2016, 04:06)Alex K Wrote: Would you believe that that exact same thing happened to me with my theory of everything? What are the odds!


Cleary, the odds are 1:1.  I assert this, can't prove it.

Boru

Well, it's easily proven. It could be true, or not, so it's clearly fifty fifty.
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition

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#15
RE: The Mathematical Proof Thread
I like the proof of Pythagoras' Theorom by inscribing a square inside another square. They share the same centre point, but the inside one is smaller and rotated slightly so that its corners touch the edges of the outer square.

By comparing the areas of the two squares and the four triangles that are produced, you can demonstrate the theorom after some slight manipulation.
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#16
RE: The Mathematical Proof Thread
The trouble is that there are many fascinating mathematical proofs, but if one has to cite 5 other obscure theorems to do it, they are no fun here.

There's a basic proof that the real numbers are not countable which is using primes which I found quite fascinating. I'll try to recall it or find it.
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition

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#17
RE: The Mathematical Proof Thread
Oh yeah, I know the one you mean Smile

Or at least, I know of one simple way to show it.
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#18
RE: The Mathematical Proof Thread
I've really liked math since 6th grade, and very recently I've started getting into it even more, at the start of our first math lecture this season my teacher came to me and my friend and slid the mathematics challenge book to us and walked away. I really need to get started with it, it seems really interesting, I haven't read much about proofs, but I'll get into it.

I'm going to start with why the heck x^0 equals 1.
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#19
RE: The Mathematical Proof Thread
(14th September 2016, 11:28)RozKek Wrote: I've really liked math since 6th grade, and very recently I've started getting into it even more, at the start of our first math lecture this season my teacher came to me and my friend and slid the mathematics challenge book to us and walked away. I really need to get started with it, it seems really interesting, I haven't read much about proofs, but I'll try to get into it.

I'm going to start with why the heck x^0 equals 1.


That seems like more a matter of definitions and making conventions compatible.

If you think of x^3: as 1•x•x•x

and x^2 as: 1•x•x

and x^1 as: 1•x

then x^0 should be simply: 1

Note that 3 isn't a factor in x^3 any more than 2 is a factor in x^2.  So there is no reason 0 should be a factor in x^0, the usual worry.  Note that every factorization includes 1 trivially.  x^1 does too.  x^0 = 1 because there are no factors of x in it at all.  But every factorization includes 1, trivially.

There are better justifications for this, but I found this way the most satisfying to students.
(16th February 2017, 18:16)TheOther JoeFish Wrote: So what you're saying is that I can harass all of the members I want for the next 168 hours, as long as I do so in my signature?
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#20
RE: The Mathematical Proof Thread
(14th September 2016, 11:38)Whateverist Wrote:
(14th September 2016, 11:28)RozKek Wrote: I've really liked math since 6th grade, and very recently I've started getting into it even more, at the start of our first math lecture this season my teacher came to me and my friend and slid the mathematics challenge book to us and walked away. I really need to get started with it, it seems really interesting, I haven't read much about proofs, but I'll try to get into it.

I'm going to start with why the heck x^0 equals 1.


That seems like more a matter of definitions and making conventions compatible.

If you think of x^3: as 1•x•x•x

and x^2 as: 1•x•x

and x^1 as: 1•x

then x^0 should be simply: 1

Note that 3 isn't a factor in x^3 any more than 2 is a factor in x^2.  So there is no reason 0 should be a factor in x^0, the usual worry.  Note that every factorization includes 1 trivially.  x^1 does too.  x^0 = 1 because there are no factors of x in it at all.  But every factorization includes 1, trivially.

There are better justifications for this, but I found this way the most satisfying to students.


heya, hoya, hoo, I'm not reading this until I give it some thought myself Tongue but thanks, I'll read this when I'm done crying
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