We have (note the convention that powers are evaluated from right to left): M(256,2,3) = ( 256 256 ) 256 256 = 256 256 257 {\displaystyle (256^{\,\!256})^{256^{256}}=256^{256^{257}}} M(256,3,3) = ( 256 256 257 ) 256 256 257 = 256 256 257 × 256 256 257 = 256 256 257 + 256 257 {\displaystyle (256^{\,\!256^{257}})^{256^{256^{257}}}=256^{256^{257}\times 256^{256^{257}}}=256^{256^{257+256^{257}}}} ≈ 256 256 256 257 {\displaystyle 256^{\,\!256^{256^{257}}}} Similarly: M(256,4,3) ≈ 256 256 256 256 257 {\displaystyle {\,\!256^{256^{256^{256^{257}}}}}} M(256,5,3) ≈ 256 256 256 256 256 257 {\displaystyle {\,\!256^{256^{256^{256^{256^{257}}}}}}} etc. Thus: mega = M ( 256 , 256 , 3 ) ≈ ( 256 ↑ ) 256 257 {\displaystyle M(256,256,3)\approx (256\uparrow )^{256}257} , where ( 256 ↑ ) 256 {\displaystyle (256\uparrow )^{256}} denotes a functional power of the function f ( n ) = 256 n {\displaystyle f(n)=256^{n}} .
우리는 다음을 알고 있다(거듭제곱이 오른쪽에서 왼쪽으로 계산하는 관습을 주목하라): M(256,2,3) = ( 256 256 ) 256 256 = 256 256 257 {\displaystyle (256^{\,\!256})^{256^{256}}=256^{256^{257}}} M(256,3,3) = ( 256 256 257 ) 256 256 257 = 256 256 257 × 256 256 257 = 256 256 257 + 256 257 {\displaystyle (256^{\,\!256^{257}})^{256^{256^{257}}}=256^{256^{257}\times 256^{256^{257}}}=256^{256^{257+256^{257}}}} ≈ 256 256 256 257 {\displaystyle 256^{\,\!256^{256^{257}}}} 유사하게: M(256,4,3) ≈ 256 256 256 256 257 {\displaystyle {\,\!256^{256^{256^{256^{257}}}}}} M(256,5,3) ≈ 256 256 256 256 256 257 {\displaystyle {\,\!256^{256^{256^{256^{256^{257}}}}}}} etc. 따라서: mega = M ( 256 , 256 , 3 ) ≈ ( 256 ↑ ) 256 257 {\displaystyle M(256,256,3)\approx (256\uparrow )^{256}257} 이고, 이 때 ( 256 ↑ ) 256 {\displaystyle (256\uparrow )^{256}} 는 함수 f ( n ) = 256 n {\displaystyle f(n)=256^{n}} 의 함수 거듭제곱을 의미한다.