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Hyperfactorial Array Notation is een erg sterke en snel groeiende functie gebaseerd op de faculteit, gemaakt door Lawrence Hollom.

HyperfaculteitEdit

Eerst definieert Lawrence Hollom de hyperfaculteit a!b als a\uparrow^{b}(a-1)\uparrow^{b}(a-2)...3\uparrow^{b}2\uparrow^{b}1, gebruik makend van pijlomhoognotatie.

ArraysEdit

1. a!b = a\uparrow^{b}(a-1)\uparrow^{b}(a-2)...3\uparrow^{b}2\uparrow^{b}1

2. a![◆,1] = a![◆] waar ◆ van alles kan zijn

3. a![b+1,◆] = ((...(a![b,◆])...)![b,◆])![b,◆] met a geneste getallen.

4. a![◇,[1],◆] = a![◇,a,◆] waar ◇ alleen enen bevat

5. a![◇,1,b,◆] = a![◇,[◇,1,1,◆],b-1,◆]

VoorbeeldenEdit

3![1] = 3!3 = 3 \uparrow^{3} 2 \uparrow^{3} 1 = 7625597484987


3![2] = ((3![1])![1])![1] = (7625597484987![1])![1] > \{3,3,1,2\}


3![1,2] = 3![[1,1],1] = 3![[1]] = 3![3] = ((3![2])![2])![2] > \{3,3,2,2\}


3![2,2] = ((3![1,2])![1,2])![1,2] > \{3,3,1,3\}


3![1,1,2] = 3![1,3] = 3![[1,1],2] = 3![[1],2] = 3![3,2] > \{3,3,2,3\}


3![2,1,2] = ((3![1,1,2])![1,1,2])![1,1,2] > \{3,3,1,1,2\}


3![1,2,2] = 3![[1,1,2],1,2] > \{3,3,1,1,3\}


3![1,1,1,2] = 3![1,1,3] = 3![[1,1,2],2,2] > \{3,3,1,1,4\}


3![2,1,3] > \{3,3,1,1,1,2\}


3![2,1,4] > \{3,3,1,1,1,1,2\}


3![2,1,1,2] = ((3![1,1,1,2])![1,1,1,2])![1,1,1,2] > \{3,3,2(1)2\}

BronnenEdit

Larwence Hollom's website

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