, , . , , . ? ? ? ? , - , , , , , , .
, , , : , ? , , ;-). , , , .
unus | - | |
duo | - | |
tres | - | |
quattuor | - | |
quinque | - | |
sex | - | |
septem | - | |
octo | - | |
novem | - | |
decem | - |
.
. : , -. "" (. mille) - (. ). , , , , , , . , , . , , 3x+3 ( x - ).
. , , , . : : -, ( 1000 ) , -. , , .. , ! , -, 6x+3 ( x - ) 6x+6 , -.
(10 9), , , . - !;-) , ( , ) , , 1000 , .. .
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, , , .. , . , .
. , , . . 1 10 33:
10 0 | |
10 1 | |
10 2 | |
10 3 | |
10 6 | |
10 9 | |
10 12 | |
10 15 | |
10 18 | |
10 21 | |
10 24 | |
10 27 | |
10 30 | |
10 33 |
, , . ? , , , , : , , , , , , , , , . , , ( . viginti ), ( . centum ) ( . mille ). ( ). , (1 000 000) decies centena milia, " ". , , :
10 63 | |
10 303 | |
10 3003 |
, , 10 3003, , ! . , -, .
10 4 | |
10 100 | |
10 140 | |
10 10100 | |
10 10 10 1000 | |
2[5] ( ) | |
10 [5] ( ) | |
2[2[5]] ( ) | |
G63 ( ) | |
G100 ( ) |
( ), , 10 000. , , , , "", , , -. , (. myriad) .
( . googol) , . "" 1938 "New Names in Mathematics" Scripta Mathematica (Edward Kasner). , "" (Milton Sirotta). , , Google. , "Google" , googol .
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-, 100 . .., ( . ), 10 140. , , .
(. googolplex) - , 10 10100. "":
Words of wisdom are spoken by children at least as often as by scientists. The name "googol" was invented by a child (Dr. Kasner's nine-year-old nephew) who was asked to think up a name for a very big number, namely, 1 with a hundred zeros after it. He was very certain that this number was not infinite, and therefore equally certain that it had to have a name. At the same time that he suggested "googol" he gave a name for a still larger number: "Googolplex." A googolplex is much larger than a googol, but is still finite, as the inventor of the name was quick to point out.
Mathematics and the Imagination (1940) by Kasner and James R. Newman.
, (Skewes' number) 1933 (Skewes. J. London Math. Soc. 8, 277-283, 1933.) , . e e e 79, eee79. , (te Riele, H. J. J. "On the Sign of the Difference (x)-Li(x)." Math. Comput. 48, 323-328, 1987) ee27/4, 8,18510 370. , e, , , , e, ..
, , Sk2, , (Sk1). , . , . Sk2 101010103, 1010101000 .
, . , , , . , . , ( ), . , ! , , ! . , , . , , , , , , , .
(H. Steinhaus. Mathematical Snapshots, 3rd edn. 1983), . , :
- nn.
- " n n ".
- " n n ".
. , .
, , , , . , , . , , . :
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- = " n " = nn = n [3].
- = " n " = n [4] = " n n " = n [3] n.
- = " n " = n [5] = " n n " = n [4] n.
- n [ k +1] = " n n k -" = n [ k ] n.
, 2[5], 10[5]. , . "2 ", 2[2[5]]. (Moser's number) .
. , - , , (Graham's number), 1977 . 64- , 1976 .
, . . . (, , , " " TeX) , , :
- 2 3 = 222.
- 8 4 = 8888.
- 2 3 = 2 2 2 = 2 4 = 65536.
- = 10 10 2.
- = 10 = 10 10 10 2.
:
, , . , G-:
- G1 = 3 .. 3, 3 3.
- G2 = .. 3, G1.
- G3 = .. 3, G2.
- ...
- G63 = .. 3, G62.
G63 ( G). " ". , , .
P.S. , . G100. , , , .
Update (4.09.2003): . , . .
- , . -, , 6,0221023 , . -, , , , . "-1", , -, , .
- rsokolov : , .
- de_kor, drw snaked , , . , :
10 000 -
100 000 -
1 000 000 -
10 000 000 -
100 000 000 -
, . " ". " ", 1050. , 1050 : " ". " ", " ", . , 10 000, , - ( ); - (10 24 ), - , ,..., , , (10 47); (10 48) , , (10 49). - , , ( , - , ):
100 - ichi
101 - jyuu
102 - hyaku
103 - sen
104 - man
108 - oku
1012 - chou
1016 - kei
1020 - gai
1024 - jyo
1028 - jyou
1032 - kou
1036 - kan
1040 - sei
1044 - sai
1048 - goku
1052 - gougasya
1056 - asougi
1060 - nayuta
1064 - fukashigi
1068 - muryoutaisuu - ( - ). botev , , , , " ". , - , , , , ( ) "3 ".
- . . , , , . , . 10 000, . "" (.. ) , . , 10 000 () , , ( ) ( ) 1063 . , 1067 ( ). :
1 = 104.
1 - = = 108.
1 - = - - = 1016.
1 - = - - = 1032.
..
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