נחשב את הערך
A
(
2
,
2
)
{\displaystyle A(2,2)}
A
(
2
,
2
)
=
A
(
1
,
A
(
2
,
1
)
)
=
A
(
1
,
A
(
1
,
A
(
1
,
0
)
)
)
=
A
(
1
,
A
(
1
,
A
(
0
,
1
)
)
)
=
A
(
1
,
A
(
1
,
2
)
)
=
A
(
1
,
A
(
0
,
A
(
1
,
1
)
)
)
=
A
(
1
,
A
(
0
,
A
(
0
,
A
(
1
,
0
)
)
)
)
=
A
(
1
,
A
(
0
,
A
(
0
,
A
(
0
,
1
)
)
)
)
=
A
(
1
,
A
(
0
,
A
(
0
,
2
)
)
)
=
A
(
1
,
A
(
0
,
3
)
)
=
A
(
1
,
4
)
=
A
(
0
,
A
(
1
,
3
)
)
=
A
(
0
,
A
(
0
,
A
(
1
,
2
)
)
)
=
A
(
0
,
A
(
0
,
A
(
0
,
A
(
1
,
1
)
)
)
)
=
A
(
0
,
A
(
0
,
A
(
0
,
A
(
0
,
A
(
1
,
0
)
)
)
)
)
=
A
(
0
,
A
(
0
,
A
(
0
,
A
(
0
,
A
(
0
,
1
)
)
)
)
)
=
A
(
0
,
A
(
0
,
A
(
0
,
A
(
0
,
2
)
)
)
)
=
A
(
0
,
A
(
0
,
A
(
0
,
3
)
)
)
=
A
(
0
,
A
(
0
,
4
)
)
=
A
(
0
,
5
)
=
6
{\displaystyle {\begin{aligned}A(2,2)&=A(1,A(2,1))\\&=A(1,A(1,A(1,0)))\\&=A(1,A(1,A(0,1)))\\&=A(1,A(1,2))\\&=A(1,A(0,A(1,1)))\\&=A(1,A(0,A(0,A(1,0))))\\&=A(1,A(0,A(0,A(0,1))))\\&=A(1,A(0,A(0,2)))\\&=A(1,A(0,3))\\&=A(1,4)\\&=A(0,A(1,3))\\&=A(0,A(0,A(1,2)))\\&=A(0,A(0,A(0,A(1,1))))\\&=A(0,A(0,A(0,A(0,A(1,0)))))\\&=A(0,A(0,A(0,A(0,A(0,1)))))\\&=A(0,A(0,A(0,A(0,2))))\\&=A(0,A(0,A(0,3)))\\&=A(0,A(0,4))=A(0,5)\\&=6\end{aligned}}}
לעומתו, ניתן לראות כי:
A
(
4
,
3
)
=
A
(
3
,
A
(
4
,
2
)
)
=
A
(
3
,
A
(
3
,
A
(
4
,
1
)
)
)
=
A
(
3
,
A
(
3
,
A
(
3
,
A
(
4
,
0
)
)
)
)
=
A
(
3
,
A
(
3
,
A
(
3
,
A
(
3
,
1
)
)
)
)
=
A
(
3
,
A
(
3
,
A
(
3
,
A
(
2
,
A
(
3
,
0
)
)
)
)
)
=
A
(
3
,
A
(
3
,
A
(
3
,
A
(
2
,
A
(
2
,
1
)
)
)
)
)
=
A
(
3
,
A
(
3
,
A
(
3
,
A
(
2
,
A
(
1
,
A
(
2
,
0
)
)
)
)
)
)
=
A
(
3
,
A
(
3
,
A
(
3
,
A
(
2
,
A
(
1
,
A
(
1
,
1
)
)
)
)
)
)
=
A
(
3
,
A
(
3
,
A
(
3
,
A
(
2
,
A
(
1
,
A
(
0
,
A
(
1
,
0
)
)
)
)
)
)
)
=
A
(
3
,
A
(
3
,
A
(
3
,
A
(
2
,
A
(
1
,
A
(
0
,
A
(
0
,
1
)
)
)
)
)
)
)
=
A
(
3
,
A
(
3
,
A
(
3
,
A
(
2
,
A
(
1
,
A
(
0
,
2
)
)
)
)
)
)
=
A
(
3
,
A
(
3
,
A
(
3
,
A
(
2
,
A
(
1
,
3
)
)
)
)
)
=
A
(
3
,
A
(
3
,
A
(
3
,
A
(
2
,
A
(
0
,
A
(
1
,
2
)
)
)
)
)
)
=
A
(
3
,
A
(
3
,
A
(
3
,
A
(
2
,
A
(
0
,
A
(
0
,
A
(
1
,
1
)
)
)
)
)
)
)
=
A
(
3
,
A
(
3
,
A
(
3
,
A
(
2
,
A
(
0
,
A
(
0
,
A
(
0
,
A
(
1
,
0
)
)
)
)
)
)
)
)
=
A
(
3
,
A
(
3
,
A
(
3
,
A
(
2
,
A
(
0
,
A
(
0
,
A
(
0
,
A
(
0
,
1
)
)
)
)
)
)
)
)
=
A
(
3
,
A
(
3
,
A
(
3
,
A
(
2
,
A
(
0
,
A
(
0
,
A
(
0
,
2
)
)
)
)
)
)
)
=
A
(
3
,
A
(
3
,
A
(
3
,
A
(
2
,
A
(
0
,
A
(
0
,
3
)
)
)
)
)
)
=
A
(
3
,
A
(
3
,
A
(
3
,
A
(
2
,
A
(
0
,
4
)
)
)
)
)
=
A
(
3
,
A
(
3
,
A
(
3
,
A
(
2
,
5
)
)
)
)
=
…
=
A
(
3
,
A
(
3
,
A
(
3
,
13
)
)
)
=
…
=
A
(
3
,
A
(
3
,
65533
)
)
=
…
=
A
(
3
,
2
65536
−
3
)
=
…
=
2
2
65536
−
3.
{\displaystyle {\begin{aligned}A(4,3)&=A(3,A(4,2))\\&=A(3,A(3,A(4,1)))\\&=A(3,A(3,A(3,A(4,0))))\\&=A(3,A(3,A(3,A(3,1))))\\&=A(3,A(3,A(3,A(2,A(3,0)))))\\&=A(3,A(3,A(3,A(2,A(2,1)))))\\&=A(3,A(3,A(3,A(2,A(1,A(2,0))))))\\&=A(3,A(3,A(3,A(2,A(1,A(1,1))))))\\&=A(3,A(3,A(3,A(2,A(1,A(0,A(1,0)))))))\\&=A(3,A(3,A(3,A(2,A(1,A(0,A(0,1)))))))\\&=A(3,A(3,A(3,A(2,A(1,A(0,2))))))\\&=A(3,A(3,A(3,A(2,A(1,3)))))\\&=A(3,A(3,A(3,A(2,A(0,A(1,2))))))\\&=A(3,A(3,A(3,A(2,A(0,A(0,A(1,1)))))))\\&=A(3,A(3,A(3,A(2,A(0,A(0,A(0,A(1,0))))))))\\&=A(3,A(3,A(3,A(2,A(0,A(0,A(0,A(0,1))))))))\\&=A(3,A(3,A(3,A(2,A(0,A(0,A(0,2)))))))\\&=A(3,A(3,A(3,A(2,A(0,A(0,3))))))\\&=A(3,A(3,A(3,A(2,A(0,4)))))\\&=A(3,A(3,A(3,A(2,5))))\\&=\ldots \\&=A(3,A(3,A(3,13)))\\&=\ldots \\&=A(3,A(3,65533))\\&=\ldots \\&=A(3,2^{65536}-3)\\&=\ldots \\&=2^{2^{\overset {65536}{}}}-3.\\\end{aligned}}}
כלומר ההפרש הוא עצום.
The Most Difficult Program to Compute?, סרטון בערוץ Computerphile באתר יוטיוב (אורך: 14:55) (באנגלית)
