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

Question

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

anonymous · Answer

$$*_k$$ is the kth new operation in this progression

anonymous · Answer

you know what, just use casio calculator lol

anonymous · Answer

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

anonymous · Answer

27 + 15 and 2 * 3, 2+2+2
27*15 and 2^3  , 2*2*2
27^15 and 2^2^2 <--- this is the new operation following exponentiation

anonymous · Answer

wow.....

nincompoop · Answer

dan, you're not telling us anything new

anonymous · Answer

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