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Brahmagupta explanation to proof on [ Negative X Negative = Positve ]




Brahmagupta explanation to proof on [ Negative X Negative = Positve ]





098. Brahmagupta explanation to proof on [ Negative X Negative = Positve ]

[ Liuhui Brahmagupta Knol 098. ]

Title : Brahmagupta explanation to proof on [ Negative X Negative = Positve ]



01. Book name

[????????????????????] (Brahma Sphuta Siddhanta, AD628, Brahmagupta)



02. Original text

??-??-??????? / Fortune - Debt - [ Sunyam( 0 ) ]

????????.???/ ???? ??-?????? ????? ???? ?????? ??-???? ???? ????

??????(Brahma) ??(18).??(33)?(Ka) : Brahma 18.33 Ka

?(ri)?(?)??(ma, **) ?(ri)?(na)-?(dha)?(na)??(ya+o=yo)??(sa, **) : rinam rina-dhanayos

??(gha-)?(?)??(sa, **) ?(dha)?(na)??(ma, **) ?(ri)?(na)??(ya+o=yo)??(sa, **) : (gha-tas) dhanam rinyos

?(dha)?(na)-?(va)?(dha)??(sa, **) ?(dha)?(na)??(ma, **) ?(bha)?(va)??(ta+i=ti) : dhana-vadhas dhanam bhavati

Brahma 18.33 Ka / rinam rina-dhanayos ghaatas dhanam rinyos dhana-vadhas dhanam bhavati



03. Word

rina = Debt, Negative number
m = (Objective, Singular)
rinam = rina (Objective, Singular)

dhana = Fortune, Credit, Money, Positive number
yos = to two things = about two things (Objective, Plural)

rina-dhanayos = to rina and dhana / about rina and dhana
ghaatas = dead

dhanam = dhana (Objective)
rinyos = to rina and rina / about rina and rina

vadhas = No, (* I have no money)
dhana-vadhas dhanam = Fortune in no fortune

bhavati = be, become, (Active, Present, Singular, Third person)



04. Literal translation

04-01. Literal translation by comparison
rinam = Debt
rina-dhanayos = to Debt and Fortune / about debt and fortune
ghaatas dhanam = Dead Fortune
rinyos = to two negatives / to negative and negative / about negative and negative
dhana-vadhas dhanam = Fortune in no fortune

04-02. Literal translation
[ Debt, to Debt and Fortune. ]
[ Dead Fortune, to two negatives, Fortune in no fortune, Be. ]



05. Simple Literal translation

[ (Debt) X (Fortune) = (Debt) ]
[ (Debt) X (Debt) = (Dead Fortune) = (Fortune in no fortune) ]



06. Original text before inversion and ellipsis

06-01. Before

On multiplication of debt and fortune,

We give debt to debt and fortune.

We give dead fortune to debt and debt

and here,

dead fortune is fortune in no fortune.


06-02. inversion and ellipsis

On multiplication of debt and fortune,

We give [ debt ] [ to debt and fortune ].

We give [ dead fortune ] [ to debt and debt ]

and here,

dead fortune [is] [ fortune in no fortune.]


06-03. After

[ debt ] [ to debt and fortune ]

[ dead fortune ] [ to debt and debt ]

[is] [ fortune in no fortune.]


06-04.

[ debt ] [ to debt and fortune ] = rinam rina-dhanayos

[ dead fortune ] [ to debt and debt ] = ghaatas dhanam rinyos

[is] [ fortune in no fortune.] = dhana-vadhas dhanam bhavati



07. Arithmetic example

[ (Debt) X (Fortune) = (Debt) ]
[ (-2) X (+3) ] = [ + { (-2) X 3 } ] = [ + (-6) ] = [ (-6) ]

[ (Debt) X (Debt) = (Dead Fortune) ]
[ (-2) X (-3) ] = [ - { (-2) X 3 } ] = [ - (-6) ] = [ + (+6) ] = [ (+6) ]

[ (Dead Fortune) = (Fortune in no fortune) ]
[ (-2) X (-3) ]is not [ + (+6) ] but [ - (-6) ].



08. Example in economic life

[ (-2) X (-3) ] [ (+2) X (+3) ]

[ - (-6) ] [ + (+6) ]

[ Subtract (Debt $6) ] [ Add (Fortune $6) ]

[ (-2) X (-3) ] is not [ Add (Fortune $6) ] but [ Subtract (Debt $6) ].



09. Law of Liuhui Brahmagupta


[ (-1) - (-1) ] = [ 0 ]
[ (+1) - (+1) ] = [ 0 ]
[ (-1) + (+1) ] = [ 0 ]
[ (+1) + (-1) ] = [ 0 ]

[ 0 ] = Sunya(0_) = Being Zero(0_) = [ (+1) + (-1) ]
[ 0 ] = Kha(_0) = Nothing = Not-being Zero(_0)

[ + (+N) ] = [ - (-N) ]
[ + (-N) ] = [ - (+N) ]

[ - N - N ] = [ - ( N + N ) ]
[ - N + N ] = [ - ( N - N ) ]

[ N X (+N) ] = [ + ( N X N) ]
[ N X (-N) ] = [ - ( N X N) ]

[ N ? (+N) ] = [ + ( N ? N ) ]
[ N ? (-N) ] = [ - ( N ? N ) ]




10. Definition of Zero ( 0 )

[ Zero ( 0 ) ] = [ Nothing ] = [ We have no (Partial Fortune and Debt) ],
[ Zero ( 0 ) is not (Nothing) but (All). ]
[ Wuji ( 0 ) ] = [ Sunyata ( 0 ) ] = [ Brahma-atma-aikya ( 0 ) ] = [ Sunya ( 0 ) ] = [ All ]

[ ( 0 ) = (Sunyata, Sunya) = (All) ] -> Never defined.
[ Sunya ( 0 ) is free from the limit of space and time. ]
[ We partially can define to use Sunya ( 0 ). ]
[ To define the thing of defining and to define Sunya ( 0 ) is right. ]
[ To define Sunya ( 0 ) and to define the thing of defining and is right. ]

On the meaning of Sunya ( 0 ) and Infinity ( ? ),
It is not the domain of (Physics, Mathematics) but the domain of (Philosophy).



11. [ 8 Definitions of Sunya ( 0 ) ], in arithmetic of Liuhui Brahmagupta

(1/9). [ Sunya ( 0 ) ] = [ (_0) ] -> Not-being ( 0 ) = (Kha) = (Nothing)
(2/9). [ Sunya ( 0 ) ] = [ (0_) ] -> Being ( 0 )
(3/9). [ Sunya ( 0 ) ] = [ (0 State of Decrease ( 0 )
(4/9). [ Sunya ( 0 ) ] = [ (0_? ) ] = [ (0_00) ] -> infinitude ( 0 )

(5/9). [ Sunya ( 0 ) ] = [ (0~) ] -> Unconsciously ( 0 ) : Financial Crisis
(6/9). [ Sunya ( 0 ) ] = [ (0--) ] -> Living Dead ( 0 ) : Legal Management
(7/9). [ Sunya ( 0 ) ] = [ (#_0) ] -> Dead ( 0 ) : Bankruptcy

(8/9). [ It is no to be measured by modern physicist ] = [ (0<) ]
(9/9). [











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