learning

Question

im teaching myself tetration and pentation because apparently I enjoy pain you guys should totally go down this rabbit hole nothing bad will come of researching Knuth's up arrow notation

math problem for you guys what is H₅ (3,6)

(H₅ is just short for hyper-5 so look that up for help)

edit: I'm now learning lambda calculus and trophs diagrams this doesn't seem too hard

Answer 1

so I did the calculations and the solution is higher than the number of atoms in the universe

Comments

i think its something like this but maybe someone who knows more can verify

H(5) (3,6)=

3↑↑↑6=

3↑↑3↑↑3↑↑3↑↑3↑↑3=

7,625,597,484,987↑↑(7,625,597,484,987↑↑7,625,597,484,987)

that double up arrow basically means that number on the left is raised to itself that number of times which is on the right

so say you have

2^^4

its 2^(2^(2^2)) or 2^(2^4) or 2^16 or 65,536

the numbers get very big very fast

so that big number in the parenthesis up there is 7,625,597,484,987 raised to 7,625,597,484,987, 7,625,597,484,987 times. we will call this number q. then you take q, and raise 7,625,597,484,987 to 7,625,597,484,987, q times. I am going to WEEP.

Answer 2

hey man my brain is officially on vacation I don't wanna do any of that stuff

Answer 3

I'm concerned for your sanity

Answer 4

umm idk