# Cantor munus bulbosum0817

Praeterea, ad diametrum rationes : Georg Cantor quoque developed per Cantor HYMENAEOS munus $$\mathbb{N}^2 \to \mathbb{W}, \quad c(x,y) = \binom{x+y+1}{2}+x = z$$ , quod si duo numeri encodes $$x,y \in \mathbb{N}$$ sunt in a numerus $$z \in \mathbb{N}$$ . Eg $$c(3,4)=\binom{3+4+1}{2}+3 = \binom{8}{2}+3=\frac{8!}{6!\cdot 2!} +3 = 31 = z$$ a unique numerus coding in a $$3$$ et $$4$$ in numero $$31$$ . Monstra: et values paro of $$\mathbb{W} = \mathbb{N}$$ , id est $$z$$ Ponit omnem numerum naturalem continet.

Nos enim probare structuram specialis ex hoc mensa:

 0 1 2 3 ... 0 0 2 5 9 ... 1 1 4 8 13 ... 2 3 7 12 18 ... 3 6 11 17 24 ... ... ... ... ... ... ...

Sic enim $$x > 0, y \geq 0$$
$$c (I + x, y) c (x, y + I), =$$
$$\ Binom {x + I + y + I} {II} + x + I - \ sinistra (\ binom {x + y + I + I} {II} + x \ rectum)) = \ binom {x + y + } {} II II - \ x + y + II binom {x} {II} + - = x + I I$$
tum quia $$x \geq 0$$
$$c (0, x + I) c (x: 0) =$$
$$\ Binom {0 + x + I + I} {II} + 0 - \ binom {x + 0 + I} {II} - x = \ binom {x + II} {II} - \ binom {x + I} {} II - x =$$
$$\ Frac {(x + II)?} {II! x!} - \ frac {(x + I)!} {II! (x-I)!} - x =$$
$$\ Frac {(x + II) (x + I),} {II} - \ frac {(x + I) x} {II} - x = \ frac {(x + I) \ sinistra ((x + II) - x \ dextra),} {} II - x = x + I - I x =$$
Id fit naturalis numeri.

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