Εισαγωγή Στην...
date post
21-Jul-2016Category
Documents
view
29download
2
Embed Size (px)
description
Μια εισαγωγή στους άπειρους αριθμούς
Transcript of Εισαγωγή Στην...
.
, , , , 2 . , , , .
2 , . , , ' , , ' . , . , . ' ; 2 , , .
' . . , {,,,} ( ) , , ,
{,} , {0,1} , {,} , {,} , {,} , {x-lnx=e,x=x} , {,} , {,} {,} ,
... ...
2 , , {{,},{0,1},{,},{,},{,},{x-lnx=e,x=x},{,},{,},,{,},...}.
. . ;' :
, , ,
, . , 17 , .
, . , . '
, , . , .
' 17 17 17 . 17 ' , ,
. , 17 17 ' ' .
:1. ' ( {,}).2. ( ), ' 1.3. ' {,},
{,} . , 2 {,} .
4. 3, . .
2 ' {,}.
;, . ; 2. ' . , ' . , , , {0,1,2,3,4,5,...,187,188,189,...,3872,3873...} N. N , 2 . 0 . R, ( ' ). R={0,1,2,3,-5,-7,0.37,,,e,262.1238764087247...}. ' R c (continuum=).
. 5 0 N. ' ' . cardA ' cardinal A. '
1 . , .
2 .
. ' , , , .
. , , .
' .
' card. cardA. card{,} {{,},{0,1},{,},{,},{,},{x-lnx=e,x=x},{,},{,},,{,},...}, 2. , , cardN=0 , cardR=c, card{,,,}=4 card{1,3,5,7,2,6,8,0}=8. cardA A3.
! , , = . , ( ) . ' ( ) Bernstain-Schrder. ' , .
. , . , =card =card, . , ' =, :
= ( !). ' ' (, !). ' , . =, .
cardZ=04. Z={...,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5...}, ' .
:
3 ' , . , , .4 , ' Z N ( , ) , , N Z (: NZ). , , , . , 5 N Z, -8 Z, 5 -8, . , 5 , . , , ' ' .
( ' 0,2,4,6,8,10,12,...) N Z, ( ' 1,3,5,7,9,11,13,...) N Z. :
N 0 1 2 3 4 5 6 7 8 ...Z 0 -1 1 -2 2 -3 2 -4 4 ...
, , cardN=cardZ cardZ=0 .
4 0.56676579805760 5 0.65778537967907 6 0.56798555680980
... 11 0.49080998090900
... 1 ' 0, 2 ' 1, 3 ' 2,..., 35 ' 34... 0.50212163273. :
' 0.23687776578478 ( 0) 1 , ' 0.09875968796875 ( 1) 2, ' 0.56786786753731 ( 2) 3, ' 0.54099522781786 ( 3) 4, ' 0.56676579805760 ( 4) 5, 0.65778537967907 ( 5) 6, ' 0.56798555680980 ( 6) 7, ... ' 0.49080998090900 ( 11) 12, ...
. ' R ' N. 0 < c.
0 , 0 .
. ' >0 < c,, c 0 ' 1. ' Cantor, Gdel Cohen . , ' (ZFC).
, . (: P())
- ' . ={1,2,3} P()={,{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}, , , . cardA
