understanding very big numbers
Interesting question which number is bigger
\[27 *_{99} 15 ~~or~~ 2*_{100} 3\]
every operation can be defined recursively in terms of its previous operations
(1)The successive operation
S(n)=n+1
(2)Addition m+n can be defined by
m+1=S(m)
m+S(n)=S(n+m)
(3) Multiplication m*n
m*1=m
m*S(n)=m+(m*n)
(4) exponentiation m^n
m^1=m
m^S(n)=m*(m^n)
(5)NewOperation
lets say we define operations in this manner
then which of these numbers is bigger
\[27 *_{99} 15~~ or~~ 2*_{100} 3\]
a link where this question and this process is explained
https://www.youtube.com/watch?v=wPEYoW0Mj1U&list=PL5A714C94D40392AB&index=139

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\[*_k\] is the kth new operation in this progression

you know what, just use casio calculator lol

we can try to see if there is pattern with the lower operations like

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