This.
Basically simplified peanut math. 1 + 1 is defined as the same thing as 2, we just write 2 because who wants to write out 1 + 1 every time.
What is 1+1? And why?
Joseph Williams
Bentley Rivera
Proof by Church encoding
+ 1 1
⇒ (λm.λn.λf.λx.m f (n f x)) (λf.λx.f x) (λf.λx.f x)
⇒ (λn.λf.λx.(λi0.λi1.i0 i1) f (n f x)) (λf.λx.f x)
⇒ λf.λx.(λi0.λi1.i0 i1) f ((λi0.λi1.i0 i1) f x)
⇒ λf.λx.(λi0.f i0) ((λi0.λi1.i0 i1) f x)
⇒ λf.λx.f ((λi0.λi1.i0 i1) f x)
⇒ λf.λx.f ((λi0.f i0) x)
⇒ λf.λx.f (f x)
⇒ 2
Isaiah Sullivan
...
Benjamin Johnson
>Now I add another (1) peanut to the location that contains my previous peanut.
That violates the Pauli exclusion principle.
Ayden Howard
Maths is independent of physics, bro.
Aiden Watson
No, it isn't.
Julian Stewart
1+1=2
Because:
3-1=2=1+1+1-1=1+1
Hope I helped.
Ethan Campbell
Exactly!
William Howard
>>Maths is independent of physics, bro.
If this is true than an illustration using an example in the physical universe is invalid and therefor the Peanut Exercise" is invalid.
Aaron Cook
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Actually this proves nothing unless one can "prove" the unfailing correlation between peanuts and real numbers. In point of fact the "Peanut Exercise" proves nothing from a mathematical standpoint...it is a simple "illustration" and not a mathematical "proof". Thus far there have been no complete proofs offered here that 1+1=2, only summaries. A complete proof would offer definitions, assumptions, proofs to support them and the equations for same. The complete proof takes up the space of a sizable book. What I have seen here thus far only "proves" that anons here can cut and paste with a fair degree of skill.