( 2) ( 4).
1. .
(" a, , Î N 0) [(a + ) + = + ( + )].
.
1) = 0, ( + ) + 0 = + (1) . ( + 0), .. ( + ) + 0 = + ( + 0).
2) , = k, .. ( + ) + k = + ( + k). , = k ', .. ( + ) + k ' = + ( + k ').
( + ) + k ' = ( (2) )
= (( + ) + k)' =( )
= ( + ( + k))' =(o (A2) )
= + ( + k)' = ( (2) )
= + ( + k ').
.. ( + ) + = + ( + ) c Î N 0, , a, Î N 0.
2.
(" a, Î N 0) [ a + = + ].
..., (" a Î N 0)[ a + 1= 1 + ].
1) = 0. 0 + 1 = 0' = 1 1 + 0 = 1 (2) . 0 + 1 = 1 + 0 .
2) , + 1 = 1 + . , ' + 1 = 1 + ',
' + 1 = ( ' = + 1)
= ( + 1) + 1 = ( )
= (1 + ) + 1 = ( )
= 1 + ( + 1) = ( + 1 = ')
= 1 + '. .. ' + 1 = 1 + ' .
, (" a Î N 0)[ a + 1 = 1 + ].
... .
1) = 0. , (" a Î N 0)[ a + 0 = 0 + ]. = 0 0 + 0 = 0 + 0 . + 0 = 0 + . , ' + 0 = 0 + '.
' + 0 = ( ' = + 1)
= ( + 1) + 0 = ( )
= + (1 + 0) = ( )
= + (0 + 1) = ( )
= ( + 0) + 1 = ( )
= (0 + ) + 1 = ( )
= 0 + ( + 1) ( + 1 = ')
= 0 + '. .. (" a Î N 0)[ a + 0 = 0 + ].
2) , = k a + k = k + . , = k ' + k ' = k ' + a.
+ k '= ( (2) )
= ( + k)' = ( ( + k)' = ( + k) + 1)
= ( + k) + 1 = ( )
= (k + a) + 1 = ( )
= k + (a + 1) = ( )
= k + (1 + a) = ( )
= (k + 1) + a = ( k + 1 = k ¢)
= k ' + . .. + = + Î N 0,
,
a, Î N 0.
, (1), (2).
(1). 0, .. (" a Î N 0) [ a 0 = 0].
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(2). (" a, Î N 0) [ a × ¢ = a + ].
, .
1. (" a, Î N 0) ($! c Î N 0)[ a × = ].
.
1) = 0 = 0 = 0 (1) .
2) , = k k , , .. a k = .
, k ¢ , a k ' = a k + = + , (. 4). , a k ' .
. , .
2. (" a, Î N 0) [ a ' = + ].
.
1) = 0 a ' 0 = 0 + 0 = a 0 + 0. .
2) , = k ' k = ak + k. , = k ' ' k ' = ak ¢ + k ¢.
' k ' = ( (2) )
= a ' k + a ' = ( )
= (ak + k) + a ' = ( ' = + 1)
= (ak + k) + (a + 1) = ( )
= (ak + ) + (k + 1) = (2 k + 1 = k ')
= ak ' + k '. , (" Î N 0) a ' = + .
... .