@a_cubed wrote:
> Whoever named the floors in Europe was a LISP programmer.

Hmmm...
(first x) ≡ (nth 0 x)

***

Now, for mathematicians, is zero a natural number?

@codinghorror

#Fortran
#Lisp
#Mathematics
#Peano

Peano, you are drunk!

#math #humour #peano #geometry

@skewray I will also add, this is all axiom based. You can derive 3 and 4 valued logic from the Peano axioms and Category Theory, no more than that is necessary.

#peano #caturday #categorytheory #twist

Provably unprovable? #WTF :-)
https://www.youtube.com/watch?v=0Le7NgS-wO0
#maths #mathematics #numbers #Goodstein #Peano #Gödel #sequence

Mi hijo (13) me ha preguntado "Si 1=2, ¿cuánto vale 1+1+1+1?" y yo he aprovechado para hablarle de los axiomas de #Peano 😋
➡️https://es.wikipedia.org/wiki/Axiomas_de_Peano

fn main() {
println!("{}", <S<S<S<S<Z>>>> as Nat>::Fact::INT);
}

#peano

gosper's graph of a space filling function painting successive range points with gradient color #hack #math #peano #lisp #mandlebrot

So which is more natural? Shapes which we see in nature or the natural numbers, which we need to define them in full?
How could #peano just assume that 0 is a natural number ? What is a shape with zero sides? Is infinity a natural number too?
What tells N from R?

- In #Peano arithmetic, second-order arithmetic and related systems, and indeed in most (not necessarily formal) mathematical treatments of the well-ordering principle, the principle is derived from the principle of mathematical induction, which is itself taken as basic

- strengthened finite #Ramsey theorem, is true, but not provable in Peano arithmetic. This was the first "natural" example of a true statement about the integers that could be stated in the language of arithmetic, but not proved in #Peano arithmetic
#godel

- Relation algebra algebraizes part of fol consisting of formulas having no atomic formula lying in scope of >3 quantifiers. Enough , for #Peano arithmetic , axiomatic set theory #ZFC; hence relation algebra, unlike PFL, is incompletable

#Peano and Mario Pieri used the expression motion for the congruence of point pairs

Hydra will eventually be killed, regardless of the strategy that Hercules uses to chop off its heads, though this may take a very long time. Just like for #Goodstein sequences, Kirby and Paris showed that it cannot be proven in #Peano arithmetic alone

Hydra will eventually be killed, regardless of the strategy that Hercules uses to chop off its heads, though this may take a very long time. Just like for #Goodstein sequences, Kirby and Paris showed that it cannot be proven in #Peano arithmetic alone

Since #Peano arithmetic cannot prove its own consistency by #Gödel's second incompleteness theorem, this shows that Peano arithmetic cannot prove the strengthened finite Ramsey theorem.

Since #Peano arithmetic cannot prove its own consistency by #Gödel's second incompleteness theorem, this shows that Peano arithmetic cannot prove the strengthened finite Ramsey theorem.

there is an integer n such that if there is a sequence of rooted trees T1, T2, ..., Tn st Tk has at most k+10 vertices, then some tree can be #homeomorphically embedded in a later one"
is provable in #Peano arithmetic, but shortest proof > A(1000), where A(0)=1 and A(n+1)=2A(n)

there is an integer n such that if there is a sequence of rooted trees T1, T2, ..., Tn st Tk has at most k+10 vertices, then some tree can be #homeomorphically embedded in a later one"
is provable in #Peano arithmetic, but shortest proof > A(1000), where A(0)=1 and A(n+1)=2A(n)

Gödel: any #recursive system that is sufficiently powerful, such as #Peano arithmetic, cannot be both consistent and syntactically complete.

Gödel: any #recursive system that is sufficiently powerful, such as #Peano arithmetic, cannot be both consistent and syntactically complete.