The Mathematical Proof Thread

[BrianSoddingBoru4]

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

[Alex K]

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!

[BrianSoddingBoru4]

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

[Alex K]

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.

[robvalue]

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.

[Alex K]

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.

[robvalue]

Oh yeah, I know the one you mean

Or at least, I know of one simple way to show it.

[RozKek]

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.

[Whateverist]

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.

[RozKek]

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 but thanks, I'll read this when I'm done crying