Veeky Forums please prove to me 2+2 = 4 in the most complex way possible

Veeky Forums please prove to me 2+2 = 4 in the most complex way possible

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cs.yale.edu/homes/as2446/224.pdf
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0.999999....=1
2(0.9...)+2(0.9...)=4

(2 + 0i) + (2 + 0i) = 4 + 0i

2+2 = 2(2) = 2^2 = 4

define 1=n+1
define 2=n+2
define 3=n+3
continue indefinitely
....
0=0 is trivially true
birds are crackers
4=n+4
2=n+2
multiply by 2
2=2n+2
move 2 to the other side
2-2=2n
divide by n
(2-2)/n = 2
from 2=n+2 2-2=n
so (2-2)/n= n/n=1
1=2
add 2 to both sides
1+2=4
but from the previous proposition, 1=2
so
2+2=4
QED

Let's use Peano axioms of addition
a+0=a (1)
a+S(b) = S(a+b) (2)
recursively define
1=S(0)
2=S(1)
3=S(2)
...
Now comes the proof
2+2=2+S(1)=S(2+1)=S(2+S(0))=S(S(2+0))=S(S(2))=S(S(S(S(0)))) which is 4 by definition of 4

2+2 is 4, minus 1 that's 3 quick maffs

Haha Fuck you, build better one.

...

Is that using Dedekind's axioms?

pic related (see Principia Mathematica pages 1 through 379 for setup to the proof)
2 + 2 = (1 + 1) + (1 + 1) = 1 + 1 + 1 + 1 = 4

I wanna kek, applaud and beat your ass at the same time

That was meant for you

Hint:
Lay out Peano Axioms.
Then you must appropriately establish addition and multiplication on the set described by these Axioms because I don't know what that strange N symbol represents.
Prove that this set equipped with these operations is a semiring.
Define 0.
1+1 =/= 1 because 1 is not an additive identity.
Prove by induction that 1 + 1 =/= n such that n is a natural number greater than 2.
Now prove that 2+2 =/= 0 and 2 + 2 =/= 1 and 2 + 2 =/= 2 and 2 + 2 =/= 3.
Then prove by induction that 2 + 2 < 5.
If 2 + 2 = z, then z must be less than 5 and greater than 3.
This leaves 4 as the only possible element that 2+2 could equal.
The details are beyond the scope of this comment and so are left to the reader.

>Veeky Forums please prove to me 2+2 = 4 in the most complex way possible

define 2
define 4

[math]2 + 2 = 1 + 1 + 1 + 1 = 4[/math]

cs.yale.edu/homes/as2446/224.pdf
And I've once heard about 2+2=4 really big proof, which was part of a bigger work, and it benefited to math - linear algebra.

i dunno, but i kek to hard

You guys are bludgering on like computers. There's literally no point AT ALL in what you guys are saying and are starting to describe. What you guys are talking about comes down to the nature of sine waves

2(2^(1/2)(Sin^2 +cos^2))^2 = 4
(2^(1/2)(Sin^2 +cos^2))^2= 2
2(2)= 4
2(2)= 2 + 2
Therefore
2 + 2 = 4

2 := x such that x+x = 4
4 := y such that 2+2 = y