One way of looking at it is this: If you multiply a positive number by a negative number the sign changes i.e. 2 x -1 = -2 So, if you multiply a negative number by a negative number, the sign *also* changes. Does this help?

Some people really do NOT get abstract math. I never did. Why a negative times a negative equals a positive will forever remain a mystery to me. Once I realized that, and understood that all I had to do was remember it, I got along a lot better in the classes. I have used this method a lot throughout my life. Especially in new jobs. Rather that asking why we did certain steps, I would learn the steps, then (unlike abstract math) for the most part, the why would reveal itself to me. Please let her know if she doesn't get the why, it is OK.

Multiplying by a positive number is adding several times. Multiplying by a negative number, by symmetry, is subtracting several times. But negative numbers are debts. If I take away (subtract) your debt, you are richer than when you started. And the more times I repeat the operation, the richer you get. So, for example, if you bank decides that they have wrongly charged you $2 (i.e. they have added -$2 to your account) 10 times, they will take away the error (-$2) 10 50,3s - or give you -$2 x -10, or +$20

how can i proof the answeer

There are lots of math proofs that explain this, and you have some really good answers here. The only thing I have to add is... I teach middle school math, and this is a little rhyme I have my students learn to remember their sign rules... When good things happen to bad people, that's bad ( + x - = -) When bad things happen to bad people, that's good (- x - = +) When bad things happen to good people, that's bad (- x + = -) When good things happen to good people, that's good ( + x + = +) It's cheesy, but it really helps them!

Explain to her that two wrongs make a right and you'll be in good shape!!

LB123. [ Negative X Negative = Positive ], Proof 1. [ N = Number ] [ Negative number = Negative = (-N) ] [ Positive number = Positive = (+N) = (N) = N ] [ Natural number = Natural ] [ Dead Zero ( 0 ) ] = [ ( 0 ) ] = [ Nothing ] [ Living Zero ( 0 ) ] = [ (+1) - (+1) ] = [ (+N) - (+N) ] = [ (+1) + (-1) ] = [ (+N) + (-N) ] = [ (-1) + (+1) ] = [ (-N) + (+N) ] = [ (-1) - (-1) ] = [ (-N) - (-N) ] [^^^] = [ (-N) = (+N) + (-2N) ] = [ (-N) = { Living Zero ( 0 ) } + (-N) ] = [ (-N) = { Living Zero ( 0 ) } - (+N) ] = [ (-N) = { (+N) - (+N) } - (+N) ] = [ (-N) = (+N) - (+N) - (+N) ] = [ (-N) = (+N) - { (+N) + (+N) } ] = [ (-N) = (+N) - { (+2N) } ] = [ (-N) = (+N) - (+2N) ] = [ (Negative) = (Subtraction of Positives) ] Change Negative for (Subtraction of Positives). [ (-N) = (+N) + (-N) + (-N) = ( 0 ) + (-N) = (+N) + (-2N) = (+N) - (+2N) ] [ (-N) ] = [ (+N) - (+2N) ] [ (-1) = (+1) + (-1) + (-1) = ( 0 ) + (-1) = (+1) + (-2) = (+1) - (+2) ] [ (-1) ] = [ (+1) - (+2) ] [ - (+N) = + (-N) ] [ - (-N) = + (+N) ] [ { - N - N } = { - ( N + N ) ] [ + N - N ] = [ - N + N ] [ ( A - B ) X ( A - B ) ] = [ ( A - B ) X A - ( A - B ) X B ] 2. Proof [^^^] = [ Negative numer X Negative number = Positive number ] = [ Negative X Negative = Positive ] = [ (Negative) X (Negative) = (Positive) ] = [ (-N) X (-N) = (+N) ] = [ { (-N) } X { (-N) } = (+N) ] = [ { (+N) + (-2N) } X { (+N) + (-2N) } = (+N) ] = [ { (+N) - (+2N) } X { (+N) - (+2N) } = (+N) ] = [ { (+N) - (+2N) } X (+N) - { (+N) - (+2N) } X (+2N) = (+N) ] = [ { (+N^2) - (+2N^2) } - { (+2N^2) - (+4N^2) } = (+N) ] = [ { (+N^2) - (+2N^2) } - { (+2N^2) + (-4N^2) } = (+N) ] = [ (+N^2) - (+2N^2) - (+2N^2) - (-4N^2) = (+N) ] = [ (+N^2) - (+2N^2) - (+2N^2) + (+4N^2) = (+N) ] = [ (+N^2) + (+4N^2) - (+2N^2) - (+2N^2) = (+N) ] = [ { (+N^2) + (+4N^2) } - { (+2N^2) + (+2N^2) } = (+N) ] = [ { (+5N^2) } - { (+4N^2) } = (+N) ] = [ (+5N^2) - (+4N^2) = (+N) ] = [ (+N^2) = (+N) ] = [ (+N) = (+N) ] = [ (N) = (N) ] = [ N = N ] 3. Example [^^^] = [ (-1) X (-1) ] = [ {(-1)} X {(-1)} ] = [ {(+1) + (-2)} X {(+1) + (-2)} ] = [ {(+1) - (+2)} X {(+1) - (+2)} ] = [ {(+1) - (+2)} X (+1) - {(+1) - (+2)} X (+2) ] = [ {(+1) - (+2)} - {(+2) - (+4)} ] = [ {(+1) - (+2)} - {(+2) + (-4)} ] = [ (+1) - (+2) - (+2) - (-4) ] = [ (+1) - (+2) - (+2) + (+4) ] = [ (+1) + (+4) - (+2) - (+2) ] = [ {(+1) + (+4)} - {(+2) + (+2)} ] = [ {(+5)} - {(+4)} ] = [ (+5) - (+4) ] = [ (+1) ] = [ (1) ] = [ 1 ] 4. Example [^^^] = [ (-2) X (-3) ] = [ { (-2) } X { (-3) } ] = [ { (+1) + (-3) } X { (+1) + (-4) } ] = [ { (+1) - (+3) } X { (+1) - (+4) } ] = [ { (+1) - (+3) } X (+1) - { (+1) - (+3) } X (+4) ] = [ { (+1) - (+3) } - { (+4) - (+12) } ] = [ { (+1) - (+3) } - { (+4) + (-12) } ] = [ (+1) - (+3) - (+4) - (-12) ] = [ (+1) - (+3) - (+4) + (+12) ] = [ (+1) + (+12) - (+3) - (+4) ] = [ { (+1) + (+12) } - { (+3) + (+4) } ] = [ { (+13) } - { (+7) } ] = [ (+13) - (+7) ] = [ (+6) ] = [ (6) ] = [ 6 ] 5. [ (-2) X (-3) ], The meaning of economic action [ (-2) X (-3) ] = [ One party of Offset, Let us Offset 3 cases in (Debt, Bill $2). ] = [ One party of Offset, Let us Offset (Debt, Bill $6). ] 6. [ (-2) X (-3) ] = [ (Debt, Bill $2) X (-3) ] = [ (Debt, Bill $2), subtract to add 3 times. ] = [ (Debt, Bill $2), subtract to multiply 3 times. ] = [ (Debt, Bill $2), come down to add 3 times. ] = [ (Debt, Bill $2), come down to multiply 3 times. ] = [ 3 cases in (Debt, Bill $2), com down. ] = [ 3 cases in (Debt, Bill $2), Let us offset. ] 7. [^^^] = [ (-2) X (-3) ] = [ - { (-2) + (-2) + (-2) } ] = [ - { (-2) X (3) } ] = [ - { (-6) } ] = [ - (-6) ] = [ + (+6) ] = [ (+6) ] = [ (6) ] = [ 6 ] LB128. Proof of Stendhal, [ (Debt 10,000 franc) X (Debt 500 franc) = (Fortune 5,000,000 franc) ] 0. Conclusion [ Offset of law of obligation ] = [ (-5,000,000) - (-5,000,000) = ( 0 ) ] [^^^] = [ (-10,000) X (-500) = - (-5,000,000) ] = [ - { (-10,000) X (500) } = - (-5,000,000) ] = [ One party of Offset, Let us Offset 500 cases in (Debt, Bill 10,000 franc). ] = [ One party of Offset, Let us Offset (Debt, Bill 5,000,000 franc). ] 1. Proof [^^^] = [ (Debt 10,000 franc ) X (Debt 500 franc) = (Fortune 5,000,000 franc) ] = [ (-10,000) X (-500) = - (-5,000,000) ] = [ { (-10,000) } X { (-500) } = - (-5,000,000) ] = [ { (+1) + (-10,001) } X { (+1) + (-501) } = - (-5,000,000) ] = [ { (+1) - (+10,001) } X { (+1) - (+501) } = (+5,000,000) ] = [ { (+1) - (+10,001) } X (+1) - { (+1) - (+10,001) } X (+501) = - (-5,000,000) ] = [ { (+1) - (+10,001) } - { (+501) - (+5,010,501) } = - (-5,000,000) ] = [ { (+1) - (+10,001) } - { (+501) + (-5,010,501) } = - (-5,000,000) ] = [ (+1) - (+10,001) - (+501) - (-5,010,501) = - (-5,000,000) ] = [ (+1) - { (+10,001) } - (+501) - (-5,010,501) = - (-5,000,000) ] = [ (+1) - { (+1) + (+10,000) } - (+501) - (-5,010,501) = - (-5,000,000) ] = [ (+1) - (+1) - (+10,000) - (+501) - (-5,010,501) = - (-5,000,000) ] = [ (+1) - (+1) + (-10,000) + (-501) - (-5,010,501) = - (-5,000,000) ] = [ (-10,000) + (-501) - (-5,010,501) = - (-5,000,000) ] = [ { (-10,000) + (-501) } - (-5,010,501) = - (-5,000,000) ] = [ { (-10,501) } - (-5,010,501) = - (-5,000,000) ] = [ (-10,501) - (-5,010,501) = - (-5,000,000) ] = [ (-10,501) - { (-5,010,501) } = - (-5,000,000) ] = [ (-10,501) - { (-10,501) + (-5,000,000) } = - (-5,000,000) ] = [ (-10,501) - (-10,501) - (-5,000,000) = - (-5,000,000) ] = [ - (-5,000,000) = - (-5,000,000) ] 2. Discovery [^^^] = [ (Debt 10,000 franc ) X (Debt 500 franc) = (Fortune 5,000,000 franc) ] = [ (-10,000) X (-500) = - (-5,000,000) ] = [ - { (-10,000) X (500) } = - (-5,000,000) ] = [ - (-5,000,000) = - (-5,000,000) ] 3. Proof [^^^] = [ (Debt 10,000 franc ) X (Debt 500 franc) = (Fortune 5,000,000 franc) ] = [ (-10,000) X (-500) = (+5,000,000) ] = [ { (-10,000) } X { (-500) } = (+5,000,000) ] = [ { (+1) + (-10,001) } X { (+1) + (-501) } = (+5,000,000) ] = [ { (+1) - (+10,001) } X { (+1) - (+501) } = (+5,000,000) ] = [ { (+1) - (+10,001) } X (+1) - { (+1) - (+10,001) } X (+501) = (+5,000,000) ] = [ { (+1) - (+10,001) } - { (+501) - (+5,010,501) } = (+5,000,000) ] = [ { (+1) - (+10,001) } - { (+501) + (-5,010,501) } = (+5,000,000) ] = [ (+1) - (+10,001) - (+501) - (-5,010,501) = (+5,000,000) ] = [ (+1) - (+10,001) - (+501) + (+5,010,501) = (+5,000,000) ] = [ (+1) + (+5,010,501) - (+10,001) - (+501) = (+5,000,000) ] = [ { (+1) + (+5,010,501) } - { (+10,001) + (+501) } = (+5,000,000) ] = [ { (+5,010,502) } - { (+10,502) } = (+5,000,000) ] = [ (+5,010,502) - (+10,502) = (+5,000,000) ] = [ (+5,000,000) = (+5,000,000) ] = [ (5,000,000) = (5,000,000) ] = [ 5,000,000 = 5,000,000 ] 4. Offset of law of obligation [^^^] = [ (-10,000) X (-500) = - (-5,000,000) ] = [ - { (-10,000) X (500) } = - (-5,000,000) ] = [ (Debt, Bill 10,000 franc), subtract thing to multiply 500 times. ] = [ (Debt, Bill 10,000 franc), subtract thing to add 500 times. ] = [ (Debt, Bill 10,000 franc), come down thing to multiply 500 times. ] = [ (Debt, Bill 10,000 franc), come down thing to add 500 times. ] = [ One party of Offset, Let us Offset 500 cases in (Debt, Bill 10,000 franc). ] = [ One party of Offset, Let us Offset (Debt, Bill 5,000,000 franc). ] 5. Conclusion [ Offset of law of obligation ] = [ (-5,000,000) - (-5,000,000) = ( 0 ) ] [^^^] = [ (-10,000) X (-500) = - (-5,000,000) ] = [ - { (-10,000) X (500) } = - (-5,000,000) ] = [ One party of Offset, Let us Offset 500 cases in (Debt, Bill 10,000 franc). ] = [ One party of Offset, Let us Offset (Debt, Bill 5,000,000 franc). ] Law of Liuhui Brahmagupta [ N X (-N) ] = [ - ( N X N ) ], [ N X (+N) ] = [ + ( N X N ) ] http://www.youtube.com/user/trapassing http://www.flickr.com/photos/trapassing I cannot english. 1/5. [ Copyright of Image and Sentence ] 2/5. Copyright Notice : Copyright © (Coupdetat.net) 3/5. Do not Editing 4/5. Free Copyright (Use Only) : Personal Homepage and Blog 5/5. Copyright (No Use) : Profit-Making, Enterprise, Government

Try using X-Y axes. Five up and five right encloses an area of 25, and five down and five left encloses an area of 25, but the upper left and lower right areas are like borrowed land--you have to give back 25 squares just to have zero. When he says he doesn't understand it, you tell her that there has to be someplace to represent borrowing, and that's it. And if she STILL doesn't understand, tell her she doesn't have to and that math is like a game where the only important thing is that the equations balance according to the rules.

[^^^] = [ (Debt $2) X 2 ] = [ (-2) X 2 ] = [ -( 2 X 2 ) ] = [ -( 4 ) ] = [ -4 ] = [ (-4) ] = [ (Debt $4) ] [^^^] = [ (Debt $2) X (Debt $2) ] = [ (-2) X (-2) ] = [ -{ 2 X (-2 ) } ] = [ -{ (-2 ) X 2 } ] = [ -{ (-4) } ] = [ - (-4) ] -----> Offset of [ Extinguishment of Obligations ], on Law of Obligations = [ + (+4) ] = [ (+4) ] = [ (4) ] = [ 4 ] = [ (Fortune $4) ]

[ A negative times a negative is a positive ], Proof in Eleven number system [ Definition of Zero ( 0 ) ] [ Zero ( 0 ) ] = [ We have no (Partial Fortune and Debt) ], on Economy [ Zero ( 0 ) ] = [ Extinguishment of Obligations ], on Law of Obligations [ Zero ( 0 ) ] = [ There is no Number ], on Arithmetic Naught number syste) : [ ( 0 ) ] = Naught Sole number syste) : [ 00000 ] Binary code, Binary number system) : [ 010101 ] decimal) : [ 12304592 ] (Single number system) + (Decimal system) = (Eleven number system) (0_) 1 2 3 4 5 6 7 8 9 0 (0_) 1 2 3 4 5 6 7 8 9 (_0) (0+) 1 2 3 4 5 6 7 8 9 (0-) Naught number system) = Dead Zero ( 0 ) Naught number system) = Not-being Zero ( 0 ) Sole number system) : [ 00000 ] = Living Zero ( 0 ) Sole number system) : [ 00000 ] = Being Zero ( 0 ) (Proof) [^^^0] = [ (-1) X (-1) = (+1) ] = [ { (-1) } X { (-1) } = (+1) ] = [ { ( 0 ) + (-1) } X { ( 0 ) + (-1) } = (+1) ] = [ { ( 0 ) - (+1) } X { ( 0 ) - (+1) } = (+1) ] = [ { ( 0 ) - (+1) } X ( 0 ) - { ( 0 ) - (+1) } X (+1) = (+1) ] = [ < { ( 0 ) X ( 0 ) } - { (+1) X ( 0 ) } > - < { ( 0 ) X (+1) } - { (+1) X (+1) } > = (+1) ] = [ < { (0_) X (_0) } - { (+1) X (_0) } > - < { (0_) X (+1) } - { (+1) X (+1) } > = (+1) ] = [ < { (_0) } - { (_0) } > - < { (0_) } - { (+1) } > = (+1) ] = [ < (_0) - (_0) > - < (0_) - (+1) > = (+1) ] = [ (_0) - (_0) - (0_) + (+1) = (+1) ] = [ - (0_) + (+1) = (+1) ] = [ - { (0_) } + (+1) = (+1) ] = [ - { (+1) - (+1) } + (+1) = (+1) ] = [ - (+1) + (+1) + (+1) = (+1) ] = [ (+1) + (+1) - (+1) = (+1) ] = [ { (+1) + (+1) } - (+1) = (+1) ] = [ { (+2) } - (+1) = (+1) ] = [ (+2) - (+1) = (+1) ] = [ (+1) = (+1) ] = [ (1) = (1) ] = [ 1 = 1 ] commutative law [^^^*] = [ (-1) X (-1) = (+1) ] = [ { (-1) } X { (-1) } = (+1) ] = [ { ( 0 ) + (-1) } X { ( 0 ) + (-1) } = (+1) ] = [ { ( 0 ) - (+1) } X { ( 0 ) - (+1) } = (+1) ] = [ { ( 0 ) - (+1) } X ( 0 ) - { ( 0 ) - (+1) } X (+1) = (+1) ] = [ < { ( 0 ) X ( 0 ) } - { (+1) X ( 0 ) } > - < { ( 0 ) X (+1) } - { (+1) X (+1) } > = (+1) ] = [ < { ^ } - { ^^ } > - < { ^^^ } - { ^^^^ } > = (+1) ] [^^^1] = [ < { ^ } - { (+1) X ( 0 ) } > - < { ( 0 ) X (+1) } - { ^^^^ } > = (+1) ] [^^^1] = [ < { ( 0 ) X ( 0 ) } - { (+1) X ( 0 ) } > - < { ( 0 ) X (+1) } - { (+1) X (+1) } > = (+1) ] = [ < { (0_) X (_0) } - { (+1) X (_0) } > - < { (0_) X (+1) } - { (+1) X (+1) } > = (+1) ] = [ < { (_0) } - { (_0) } > - < { (0_) } - { (+1) } > = (+1) ] = [ < (_0) - (_0) > - < (0_) - (+1) > = (+1) ] = [ (_0) - (_0) - (0_) + (+1) = (+1) ] = [ - (0_) + (+1) = (+1) ] = [ - { (0_) } + (+1) = (+1) ] = [ - { (+1) - (+1) } + (+1) = (+1) ] = [ - (+1) + (+1) + (+1) = (+1) ] = [ (+1) + (+1) - (+1) = (+1) ] = [ { (+1) + (+1) } - (+1) = (+1) ] = [ { (+2) } - (+1) = (+1) ] = [ (+2) - (+1) = (+1) ] = [ (+1) = (+1) ] [^^^2] = [ < { ^ } - { ( 0 ) X (+1) } > - < { ( 0 ) X (+1) } - { ^^^^ } > = (+1) ] [^^^2] = [ < { ( 0 ) X ( 0 ) } - { ( 0 ) X (+1) } > - < { ( 0 ) X (+1) } - { (+1) X (+1) } > = (+1) ] = [ < { (0_) X (_0) } - { (0_) X (+1) } > - < { (0_) X (+1) } - { (+1) X (+1) } > = (+1) ] = [ < { (_0) } - { (0_) } > - < { (0_) } - { (+1) } > = (+1) ] = [ < (_0) - (0_) > - < (0_) - (+1) > = (+1) ] = [ (_0) - (0_) - (0_) + (+1) = (+1) ] = [ - (0_) - (0_) + (+1) = (+1) ] = [ - { (0_) } - { (0_) } + (+1) = (+1) ] = [ - { (+1) - (+1) } - { (+1) - (+1) } + (+1) = (+1) ] = [ - (+1) + (+1) - (+1) + (+1) + (+1) = (+1) ] = [ (+1) + (+1) + (+1) - (+1) - (+1) = (+1) ] = [ { (+1) + (+1) + (+1) } - { (+1) + (+1) } = (+1) ] = [ { (+3) } - { (+2) } = (+1) ] = [ (+3) - (+2) = (+1) ] = [ (+1) = (+1) ] [^^^3] = [ < { ^ } - { (+1) X ( 0 ) } > - < { (+1) X ( 0 ) } - { ^^^^ } > = (+1) ] [^^^3] = [ < { ( 0 ) X ( 0 ) } - { (+1) X ( 0 ) } > - < { (+1) X ( 0 ) } - { (+1) X (+1) } > = (+1) ] = [ < { (0_) X (_0) } - { (+1) X (_0) } > - < { (+1) X (_0) } - { (+1) X (+1) } > = (+1) ] = [ < { (_0) } - { (_0) } > - < { (_0) } - { (+1) } > = (+1) ] = [ < (_0) - (_0) > - < (_0) - (+1) > = (+1) ] = [ (_0) - (_0) - (_0) + (+1) > = (+1) ] = [ (+1) > = (+1) ] [^^^4] = [ < { ^ } - { ( 0 ) X (+1) } > - < { (+1) X ( 0 ) } - { ^^^^ } } > = (+1) ] [^^^4] = [ < { ( 0 ) X ( 0 ) } - { ( 0 ) X (+1) } > - < { (+1) X ( 0 ) } - { (+1) X (+1) } > = (+1) ] = [ < { (0_) X (_0) } - { (0_) X (+1) } > - < { (+1) X (_0) } - { (+1) X (+1) } > = (+1) ] = [ < { (_0) } - { (0_) } > - < { (_0) } - { (+1) } > = (+1) ] = [ < (_0) - (0_) > - < (_0) - (+1) > = (+1) ] = [ (_0) - (0_) - (_0) + (+1) = (+1) ] = [ - (0_) + (+1) = (+1) ] = [ - { (0_) } + (+1) = (+1) ] = [ - { (+1) - (+1) } + (+1) = (+1) ] = [ - (+1) + (+1) + (+1) = (+1) ] = [ (+1) + (+1) - (+1) = (+1) ] = [ { (+1) + (+1) } - (+1) = (+1) ] = [ { (+2) } - (+1) = (+1) ] = [ (+2) - (+1) = (+1) ] = [ (+1) = (+1) ] Coupdetat.net (2009.04.12)

Ok .. Think about the basics of multipication. When you multiply a positive number by a positive number you are adding groups of the same together....2*3=0+3+3=6 When you are multiplying a positive number by a negative number you are still adding groups together.. 2*-3=0+(-3)+(-3)=-6 However when you are multiplying a negative by a negative.. you are taking away groups -2*-3=0-(-3)-(-3)=6 Oh and with fractions..this again involves adding or taking away groups or in the case of fraction * another fraction, the adding or taking away of (fractions of groups). Some examples: -number*+number with fractions 2*(-1/2)=0+(-1/2)+(-1/2)=-1 With negative fraction multiplied by another negative you are taking away groups (-1/2)*(-2)=0-(-1/2)-(-1/2)=1 so the - in (-2) just means take away groups starting from 0. Therefore (-2/3)*(-1/3)=0-(2/3 of -1/3)=0-(-2/9)=2/9

multiplication [ (0_) = ( 0 ) ] The Movement in multiplication Field of Fortune and Debt, they are as follows. [ (0_)(0_) = ( 0 ) ] (1/4) = Increase of Fortune = Increase of Positive number = [ (+2) X (+3) ] = [ (+6) ] (2/4) = Decrease of Debt = Decrease of Negative number = [ (-2) X (-3) ] = [ (+6) ] (3/4) = Increase of Debt = Increase of Negative number = [ (-2) X (+3) ] = [ (-6) ] (4/4) = Decrease of Fortune = Decrease of Positive number = [ (+2) X (-3) ] = [ (-6) ] [ (0_)(0_)(0_) = ( 0 ) ] [^^^] = [ (1/4) ] = [ Increase of Fortune (Money $2), 3 times. ] = [ + { (Fortune, Money $2) + (Fortune, Money $2) + (Fortune, Money $2) } ] = [ + { (+2) + (+2) + (+2) } ] = [ + { (Fortune, Money $2) X 3 } ] = [ + { (+2) X 3 } ] = [ { (+2) X (+3) } ] = [ (+2) X (+3) ] = [ (+2) X (<+>3) ] The meaning of <+> is not Fortune but Adding sign(+). [^^^] = [ (2/4) ] = [ Decrease of Debt (Money $2), 3 times. ] = [ - { (Debt, Money $2) + (Debt, Money $2) + (Debt, Money $2) } ] = [ - { (-2) + (-2) + (-2) } ] = [ - { (Debt, Money $2) X 3 } ] = [ - { (-2) X 3 } ] = [ { (-2) X (-3) } ] = [ (-2) X (-3) ] = [ (-2) X (<->3) ] The meaning of <-> is not Debt but Subtraction sign(-). [^^^] = [ (3/4) ] = [ Increase of Debt (Money $2), 3 times. ] = [ + { (Debt, Money $2) + (Debt, Money $2) + (Debt, Money $2) } ] = [ + { (-2) + (-2) + (-2) } ] = [ + { (Debt, Money $2) X 3 } ] = [ + { (-2) X 3 } ] = [ { (-2) X (+3) } ] = [ (-2) X (+3) ] = [ (-2) X (<+>3) ] The meaning of <+> is not Fortune but Adding sign(+). [^^^] = [ (4/4) ] = [ Decrease of Fortune (Money $2), 3 times. ] = [ - { (Fortune, Money $2) + (Fortune, Money $2) + (Fortune, Money $2) } ] = [ - { (+2) + (+2) + (+2) } ] = [ - { (Fortune, Money $2) X 3 } ] = [ - { (+2) X 3 } ] = [ { (+2) X (-3) } ] = [ (+2) X (-3) ] = [ (+2) X (<->3) ] The meaning of <-> is not Debt but Subtraction sign(-). [ (0_)(0_)(0_)(0_) = ( 0 ) ] Proof of [ (Positive) X (Positive) = (Positive) ] [^^^] = [ (1/4) ] = [ Increase of Fortune (Money $2), 3 times. ] = [ (+2) X (+3) ] = [ (+2) X 3 ] = [ + { (+2) X 3 } ] = [ (+2) X 3 ] = [ + { (+6) } ] = [ (+6) ] = [ + (+6) ] = [ (+6) ] = [ (+6) ] = [ (+6) ] = [ <+> (+6) ] = [ (+6) ] The meaning of <+> is not not Adding sign(+) but (Adding up). Proof of [ (Negative) X (Negative) = (Positive) ] [^^^] = [ (2/4) ] = [ Decrease of Debt (Money $2), 3 times. ] = [ (-2) X (-3) ] = [ - (-6) ] = [ { (-2) } X { (-3) } ] = [ - (-6) ] = [ { (+1) + (-3) } X { (+1) + (-4) } ] = [ - (-6) ] = [ { (+1) - (+3) } X { (+1) - (+4) } ] = [ - (-6) ] = [ { (+1) - (+3) } X (+1) - { (+1) - (+3) } X (+4) ] = [ - (-6) ] = [ { < (+1) X (+1) > - < (+3) X (+1) > } - { < (+1) X (+4) > - < (+3) X (+4) > } ] = [ - (-6) ] = [ { < + [ (+1) X 1 ] > - < + [ (+3) X 1 ] > } - { < + [ (+1) X 4 ] > - < + [ (+3) 4 ] > } ] = [ - (-6) ] = [ { < [ (+1) X 1 ] > - < [ (+3) X 1 ] > } - { < [ (+1) X 4 ] > - < [ (+3) 4 ] > } ] = [ - (-6) ] = [ { < (+1) X 1 > - < (+3) X 1 > } - { < (+1) X 4 > - < (+3) X 4 > } ] = [ - (-6) ] = [ { < (+1) > - < (+3) > } - { < (+4) > - < (+12) > } ] = [ - (-6) ] = [ { (+1) - (+3) } - { (+4) - (+12) } ] = [ - (-6) ] = [ (+1) - (+3) - (+4) + (+12) ] = [ - (-6) ] = [ (+1) + (+12) - (+3) - (+4) ] = [ - (-6) ] = [ { (+1) + (+12) } - { (+3) + (+4) } ] = [ - (-6) ] = [ { (+13) } - { (+7) } ] = [ - (-6) ] = [ (+13) - (+7) ] = [ - (-6) ] = [ (+6) ] = [ - (-6) ] = [ + (+6) ] = [ - (-6) ] = [ - (-6) ] = [ - (-6) ] = [ + (+6) ] = [ + (+6) ] = [ (+6) ] = [ (+6) ] = [ (6) ] = [ (6) ] = [ 6 ] = [ 6 ] Proof of [ (Negative) X (Positive) = (Negative) ] [^^^] = [ (3/4) ] = [ Increase of Debt (Money $2), 3 times. ] = [ (-2) X (+3) ] = [ { (-2) } X (+3) ] = [ { (+1) + (-3) } X (+3) ] = [ { (+1) - (+3) } X (+3) ] = [ { (+1) X (+3) } - { (+3) X (+3) } ] = [ { + < (+1) X 3 > } - { + < (+3) X 3 > } ] = [ { < (+1) X 3 > } - { < (+3) X 3 > } ] = [ { < (+3) > } - { < (+9) > } ] = [ { (+3) } - { (+9) } ] = [ (+3) - (+9) ] = [ (+3) + (-9) ] = [ (-9) + (+3) ] = [ (-9) - (-3) ] = [ (-6) ] Proof of [ (Positive) X (Negative) = (Negative) ] [^^^] = [ (4/4) ] = [ Decrease of Fortune (Money $2), 3 times. ] = [ (+2) X (-3) ] = [ (+2) X { (-3) } ] = [ (+2) X { (+1) + (-4) } ] = [ (+2) X { (+1) - (+4) } ] = [ { (+2) X (+1) } - { (+2) X (+4) } ] = [ { + < (+2) X 1 > } - { + < (+2) X 4 > } ] = [ { < (+2) X 1 > } - { < (+2) X 4 > } ] = [ { (+2) X 1 } - { (+2) X 4 } ] = [ { (+2) } - { (+8) } ] = [ (+2) - (+8) ] = [ (+2) + (-8) ] = [ (-8) + (+2) ] = [ (-8) - (-2) ] = [ (-6) ] [ (0_)(0_)(0_)(0_)(0_) = ( 0 ) ] [ Number = N ] [ Negative number = Negative = (-N) ] [ Positive number = Positive = (+N) = N ] [^^^] = [ (+N) X (+N) ] = [ + { (+N) X N } ] * = [ { (+N) X N } ] = [ (+N) X N ] = [+(N^2)] = [(N^2)] [^^^] = [ (-N) X (-N) ] = [ - { (-N) X N } ] * = [ - {-(N^2)} ] = [ + {+(N^2)} ] = [ {+(N^2)} ] = [ {(N^2)} ] = [ (N^2) ] [^^^] = [ (-N) X (+N) ] = [ + { (-N) X N } ] * = [ { (-N) X N } ] = [ (-N) X N ] = [-(N^2)] [^^^] = [ (+N) X (-N) ] = [ - { (+N) X N } ] * = [ - {+(N^2)} ] = [ + {-(N^2)} ] = [ {-(N^2)} ] = [-(N^2)] Coupdetat.net (2009.04.19)

LB244. (Adding up) and (Sophistry) on [ (Negative) X (Negative) = (Positive) ] (Adding up) and (Sophistry) on [ (Negative) X (Negative) = (Positive) ] ( 00 ). Proof of [ (Negative) X (Negative) = (Positive) ] by (Adding up) and Sophistry. (01). Zero ( 0 ) In proof of [ (Negative) X (Negative) = (Positive) ], surely, proofs(direct, indirect, complex plane) ask Zero ( 0 ) for (Being) and (Definition). (02). (Adding up) Proof of (Adding up) do not ask Zero ( 0 ) for (Being) and (Definition). Kernel of proof is (Adding up = add to collect). (Adding up) is free of death and life. [^^^] = [ + (+2) ] = [ <+> (+2) ] <+> = meaning of (Adding up) (03). 2 meanings of addition sign(+) 1-2. Simply add : (Example) [ 2 + 3 = 5 ] 2-2. Adding up 2-2-1. (Havings) 2-2-1-1. In left pocket, (Money, $2) 2-2-1-2. In right pocket, (Money, $3) 2-2-1-3. No debt 2-2-2. (Leavings) 2-2-2-1. How much is it altogether? 2-2-2-2-1. [ (Leavings) = (Money, $2) + (Money, $3) + (No debt) ] 2-2-2-2-2. [ (Leavings) = (Money, $2) <+> (Money, $3) <+> (No debt) ] 2-2-2-2-3. [ (Leavings) = (Money, $5) ] 2-2-2-2-4. [ <+> = meanings of (Adding up) ] 2-2-2-2-5. [ <+> = (Adding up) = (add to collect) ] 2-2-2-2-6. (Adding up) is free of death and life. 2-2-2-2-7. [ - (-2) ] = [ + (+2) ] = [ (+2) ] = [ (2) ] = [ 2 ] 2-2-2-2-8. [ - (+2) ] = [ + (-2) ] = [ (-2) ] (04). Signs (Shu) = (Number) = (N) (WuShu) = (Sunya) = (Zero) = [ ( 0 ) ] = ( â–¡ ) = ( ● ) (FuShu) = (Rina) = (Obligation) = (Debt) = (Bill) = (Negative number) = (Negative) = [ (-N) ] (ZhengShu) = (Dhana) = (Fortune) = (Credit) = (Money) = (Positive number) = (Positive) = [ (+N) ] (Add) = (Addition Sign) = (+) (Subtract) = (Subtraction Sign) = (-) (Mutiply) = (Multiplication Sign) = (X) = (x) = (Ë™) = (.) = (*) = (Omission) (Divide) = (Division Sign) = (÷) = (/) (05). Conclusion [^^^] = [ Add, (Debt $6) ] = [ Subtract, (Fortune $6) ] = [ (Debt $6) ] = [ + (-6) ] = [ - (+6) ] = [ (-6) ] = [ + { (-6) } ] = [ - { (+6) } ] = [ + { (-2) + (-2) + (-2) } ] = [ - { (+2) + (+2) + (+2) } ] = [ + { (-2) X 3 } ] = [ - { (+2) X 3 } ] = [ + { (-2) X (3) } ] = [ - { (+2) X (3) } ] = [ { (-2) X (+3) } ] = [ { (+2) X (-3) } ] = [ (-2) X (+3) ] = [ (+2) X (-3) ] * [ (-N) X (+N) ] = [ + { (-N) X N } ] * [ (+N) X (-N) ] = [ - { (+N) X N } ] * [ (-N) X (-N) ] = [ - { (-N) X N } ] = [ - { (-N^2) } ] = [ - (-N^2) ] = [ + (+N^2) ] = [ (+N^2) ] = [ (N^2) ] = [ N^2 ] = [ N X N ] (06). [^^^] = [ (+2) ] = [ (Fortune $2) ] = [ + (+2) ] = [ + (Fortune $2) ] = [ Add, (Fortune $2) ] = [ + (2) ] = [ (2) ] = [ 2 ] (07). [^^^] = [ (+3) ] = [ (Fortune $3) ] = [ + (+3) ] = [ + (Fortune $3) ] = [ Add, (Fortune $3) ] = [ + (3) ] = [ (3) ] = [ 3 ] (08). [^^^] = [ (+6) ] = [ (Fortune $6) ] = [ + (+6) ] = [ Add, (Fortune $6) ] = [ + { (+6) } ] = [ Add, { (Fortune $6) } ] = [ + {(+2)+(+2)+(+2)}] = [Add,{(Fortune $2)+(Fortune $2)+(Fortune $2)}] = [ + { (+2) X 3 } ] = [ Add, { (Fortune $2) X 3 } ] = [ + { (+2) X (3) } ] = [ Add, { (Fortune $2) X (3) } ] = [ { (+2) X (+3) } ] = [ { (Fortune $2) X (Fortune $3) } ] = [ (+2) X (+3) ] = [ (Fortune $2) X (Fortune $3) ] = [ (+N) X (+N) ] = [ + { (+N) X N } ] (09). [^^^] = [ (+2) X (+3) ] = [ (Fortune $2) X (Fortune $3) ] = [ (+2) X (+3) ] = [ (Positive) X (Positive) ] = [ + { (+2) X (3) } ] = [ Add, { (Fortune $2) X (3) } ] = [ + { (+2) X 3 } ] = [ Add, { (Fortune $2) X 3 } ] = [ + { (+6) } ] = [ Add, { (Fortune $6) } ] = [ { (+6) } ] = [ { (Fortune $6) } ] = [ (+6) ] = [ (Fortune $6) ] = [ (6) ] = [ (Fortune $6) ] = [ 6 ] = [ (Fortune $6) ] (10). [^^^] = [ (-6) ] = [ (Debt $6) ] = [ + (-6) ] = [ Add, (Debt $6) ] = [ + { (-6) } ] = [ Add, { (Debt $6) } ] = [ + { (-2) + (-2) + (-2) } ]=[Add,{(Debt $2)+(Debt $2)+(Debt $2)}] = [ + { (-2) X 3 } ] = [ Add, { (Debt $2) X 3 } ] = [ + { (-2) X (3) } ] = [ Add, { (Debt $2) X (3) } ] = [ { (-2) X (+3) } ] = [ { (Debt $2) X (Fortune $3) } ] = [ (-2) X (+3) ] = [ (Debt $2) X (Fortune $3) ] = [ (-N) X (+N) ] = [ + { (-N) X N } ] (11). [^^^] = [ (-2) X (+3) ] = [ (Debt $2) X (Fortune $3) ] = [ (-2) X (+3) ] = [ (Negative) X (Positive) ] = [ + { (-2) X (3) } ] = [ Add, { (Debt $2) X (3) } ] = [ + { (-2) X 3 } ] = [ Add, { (Debt $2) X 3 } ] = [ + { (-6) } ] = [ Add, { (Debt $6) } ] = [ { (-6) } ] = [ { (Debt $6) } ] = [ (-6) ] = [ (Debt $6) ] (12). [^^^] = [ + (-6) ] = [ - (+6) ] = [ (-6) ] = [ Add, (Debt $6) ] = [ Subtract, (Fortune $6) ] = [ (Debt $6) ] = [ + (-6) ] = [ - (+6) ] = [ + { (-6) } ] = [ - { (+6) } ] = [ + { (-2) + (-2) + (-2) } ] = [ - { (+2) + (+2) + (+2) } ] = [ + { (-2) X 3 } ] = [ - { (+2) X 3 } ] = [ + { (-2) X (3) } ] = [ - { (+2) X (3) } ] = [ { (-2) X (+3) } ] = [ { (+2) X (-3) } ] = [ (-2) X (+3) ] = [ (+2) X (-3) ] = [ (+N) X (-N) ] = [ - { (+N) X N } ] (13). [^^^] = [ (-2) X (+3) ] = [ (+2) X (-3) ] = [ + { (-2) X (3) ] = [ - { (+2) X (3) } ] = [ + { (-2) X 3 ] = [ - { (+2) X 3 } ] = [ + { (-6) } ] = [ - { (+6) } ] = [ + (-6) ] = [ - (+6) ] = [ + (-6) ] = [ + (-6) ] = [ (-6) ] = [ (-6) ] (14). [^^^] = [ N X (+N) ] = [ + { N X N } ] [^^^] = [ N X (-N) ] = [ - { N X N } ] [^^^] = [ (+N) X (+N) ] = [ + { (+N) X N } ] [^^^] = [ (-N) X (+N) ] = [ + { (-N) X N } ] [^^^] = [ (+N) X (-N) ] = [ - { (+N) X N } ] (15). [^^^] = [ (Negative) X (Negative) = (Positive) ] = ( ? ) Basis on proof is [ N X (-N) ] = [ - { N X N } ]. [^^^] = [ (-2) X (-3) ] = [ (+2) X (+3) ] = [ { (-2) X (-3) } ] = [ { (+2) X (+3) } ] = [ - { (-2) X (3) } ] = [ + { (+2) X (3) } ] = [ - { (-2) X 3 } ] = [ + { (+2) X 3 } ] = [ - { (-6) } ] = [ + { (+6) } ] = [ - (-6) ] = [ + (+6) ] = [ + (+6) ] = [ + (+6) ] = [ (+6) ] = [ (+6) ] = [ (6) ] = [ (6) ] = [ 6 ] = [ 6 ] (16). [^^^] = [ (-2) X (-3) ] = [ (+2) X (+3) ] = [ (Debt $2) X (Debt $3) ] = [ (Fortune $2) X (Fortune $3) ] = [ Subtract a thing that (Debt $2) added, 3 times. ] = [Add a thing that (Fortune $2) added, 3 times. ] = [ One party of Offset ] = [ (Fortune $6) ] (17). Conclusion, [^^^] = [ N X (+N) ] = [ + { N X N } ] [^^^] = [ N X (-N) ] = [ - { N X N } ] (18). [^^^] = [ N ÷ (+N) ] = [ N X (+1/N) ] = [ + { N X (1/N) } ] = [ + { N ÷ N } ] [^^^] = [ N ÷ (-N) ] = [ N X (-1/N) ] = [ - { N X (1/N) } ] = [ - { N ÷ N } ] (19). [^^^] = [ (-N) ÷ (-N) ] = [ (-N) X (-1/N) ] = [ - { (-N) X (1/N) } ] = [ - { (-N) ÷ N } ] = [ - { (-1) } ] = [ - (-1) ] = [ + (+1) ] = [ (+1) ] = [ (1) ] = [ 1 ] (20). (Division) is reverse calculation of multiplication. [^^^] = [ (Positive) X (Positive) = (Positive) ] = [ (Positive) = (Positive) ÷ (Positive) ] [^^^] = [ (Negative) X (Positive) = (Negative) ] = [ (Negative) = (Negative) ÷ (Positive) ] [^^^] = [ (Positive) X (Negative) = (Negative) ] = [ (Positive) = (Negative) ÷ (Negative) ] [^^^] = [ (Negative) X (Negative) = (Positive) ] -> Offset = [ (Negative) = (Positive) ÷ (Negative) ] -> Partnership, Offset ----------------------------------------------------------- (21). Sophistry, [ (-1) X (-A) = <-(-A)> ] [^^^] = [ (-1) X A = (-A) ] [^^^] = [ (-1) X (-A) = -(-A) ] = [ (-1) X (-A) = <-(-A)> ] [^^^] = [ (-1)A = (-A) ] [^^^] = [ (-1)(-A) = -(-A) ] = [ (-1)(-A) = <-(-A)> ] [^^^] = [ (-1) X (+A) = (-A) ] [^^^] = [ (-1) X (-A) = -(-A) ] = [ (-1) X (-A) = <-(-A)> ] = [ (Negative) X (Negative) = (Positive) ] It is looked like right, but sophistries. [^^^] = [ <-(-A)> ] = [ <Negative sign(Negative A)> ] ---> Sophistry [^^^] = [ (-1) X (+A) ] = [ + { (-1) X A } ] = [ + { (-A) } ] = [ + (-A) ] = [ (-A) ] [^^^] = [ (-1) X (-A) ] = [ - { (-1) X (A) } ] = [ - { (-1) X A } ] = [ - { (-A) } ] = [ - (-A) ] = [ Subtraction sign (Negative A) ] = [ + (+A) ] = [ (+A) ] = [ (A) ] = [ A ] [ <Negative sign(Negative A)> ] <--- (differ) ----> [ Subtraction sign (Negative A) ] therefore, Sophistry. [ <-(-A)> ] <--- (differ) ----> [ - (-A) ] therefore, Sophistry. Coupdetat.net (2009.04.28)

[ (-4) X (-3) ] = [ (+12) ], Proof http://blog.naver.com/popuri81/70000259014 [^^^] = [ (-3) + (+3) = ( 0 ) ], [ (-4) + (+4) = ( 0 ) ] = [ { (-3) + (+3) } = ( 0 ) ], [ { (-4) + (+4) } = ( 0 ) ] = [ {(-3) + (+3)} X (+4) = ( 0 ) X (+4) ], [ {(-4) + (+4)} X (-3) = ( 0 ) X (-3) ] = [ {(-3) X (+4)} + {(+3) X (+4)} = ( 0 ) ], [ {(-4) X (-3)} + {(+4) X (-3)} = ( 0 ) ] = [ {(+3) X (+4)} = ( 0 ) - {(-3) X (+4)} ], [ {(-4) X (-3)} = ( 0 ) - {(+4) X (-3)} ] = [ {(+3) X (+4)} = ( 0 ) - {(-12)} ], [ {(-4) X (-3)} = ( 0 ) - {(-12)} ] = [ {(+3) X (+4)} = ( 0 ) - (-12) ], [ {(-4) X (-3)} = ( 0 ) - (-12) ] = [ {(+3) X (+4)} = ( 0 ) + (+12) ], [ {(-4) X (-3)} = ( 0 ) + (+12) ] = [ {(+3) X (+4)} = (+12) ], [ {(-4) X (-3)} = (+12) ] = [ {(+3) X (+4)} = (+12) ], [ (+12) = {(-4) X (-3)} ] = [ {(+3) X (+4)} = (+12) = {(-4) X (-3)} ] = [ {(+3) X (+4)} = (12) = {(-4) X (-3)} ] = [ {(+3) X (+4)} = 12 = {(-4) X (-3)} ] = [ {(+3) X (+4)} = {(-4) X (-3)} ] = [ (+3) X (+4) = (-4) X (-3) ] Proof of Liuhui Brahmagupta [^^^] = [ N X (-N) ] = [ - { N X N } ] = [ (-4) X (-3) ] = [ - { (-4) X (3) ] = [ - { (-4) X 3 ] = [ - { (-12) } ] = [ - (-12) ] = [ + (+12) ] = [ (+12) ] = [ (12) ] = [ 12 ] [^^^] = [ (-4) X (-3) ] = [ { (-4) } X { (-3) } ] = [ { (+1) + (-5) } X { (+1) + (-4) } ] = [ { (+1) - (+5) } X { (+1) - (+4) } ] = [ { (1) - (5) } X { (1) - (4) } ] = [ { 1 - 5 } X { 1 - 4 } ] = [ < { 1 X 1 } - { 5 X 1 } > - < { 1 X 4 } - { 5 X 4 } > ] = [ < { 1 } - { 5 } > - < { 4 } - { 20 } > ] = [ < 1 - 5 > - < 4 - 20 > ] = [ 1 - 5 - 4 + 20 ] = [ 1 + 20 - 5 - 4 ] = [ ( 1 + 20 ) - ( 5 + 4 ) ] = [ ( 21 ) - ( 9 ) ] = [ 21 - 9 ] = [ 12 ] = [ (12) ] = [ (+12) ]

[ Open discussion for learning of Arithmetic-002. ] [ (-1) X (-1) ] = [ 1 ], Proof (Direct) Proof, (Source) http://gall.dcinside.com/list.php?id=warcraft&no=1052249 [^^^] = [ (-1) X (-1) ] = [ { (-1) X (-1) } + ( 0 ) ] = [ { (-1) X (-1) } + { ( 0 ) } ] -----> Living ( 0 ) = [ { (-1) X (-1) } + { (-1) + (+1) } ] ---> Dead ( 0 ) = [ { (-1) X (-1) } + { < (-1) > + (+1) } ] = [ { (-1) X (-1) } + { < (-1) X (+1) > + (+1) } ] = [ { (-1) X (-1) } + < (-1) X (+1) > + (+1) ] = [ { (-1) X < (-1) + (+1) > } + (+1) ] = [ { (-1) X < ( 0 ) > } + (+1) ] = [ { (-1) X ( 0 ) } + (+1) ] = [ { ( 0 ) } + (+1) ] = [ ( 0 ) + (+1) ] = [ (+1) ] = [ (1) ] = [ 1 ] Proof of Liuhui Brahmagupta [^^^] = [ N X (-N) ] = [ - { N X N } ] = [ (-1) X (-1) ] = [ - { (-1) X (1) ] = [ - { (-1) X 1 ] = [ - { (-1) } ] = [ - (-1) ] = [ + (+1) ] = [ (+1) ] = [ (1) ] = [ 1 ] [^^^] = [ (-1) X (-1) ] = [ { (-1) } X { (-1) } ] = [ { (+1) + (-2) } X { (+1) + (-2) } ] = [ { (+1) - (+2) } X { (+1) - (+2) } ] = [ { (1) - (2) } X { (1) - (2) } ] = [ { 1 - 2 } X { 1 - 2 } ] = [ < { 1 X 1 } - { 2 X 1 } > - < { 1 X 2 } - { 2 X 2 } > ] = [ < { 1 } - { 2 } > - < { 2 } - { 4 } > ] = [ < 1 - 2 > - < 2 - 4 > ] = [ 1 - 2 - 2 + 4 ] = [ 1 + 4 - 2 - 2 ] = [ ( 1 + 4 ) - ( 2 + 2 ) ] = [ ( 5 ) - ( 4 ) ] = [ 5 - 4 ] = [ 1 ] = [ (1) ] = [ (+1) ] Coupdetat.net (2009.04.28)

LB304. Logicality of sophistry 1. Sophistry [ (-1) X 1 ] = [ (-1) ] [ (-1) X (-1) ] = [-(-1)] [-(-1)] = [ Negative sign(Negative sign1) ] -> Sophistry 2. [-(-1)] = [ Negative sign(Negative sign1) ] -> Example ? 3. [ + (-1) ] = [ - (+1) ] [ <+> (-1) ] = [ - (<+>1) ] [ Add -sign ] = [ Positive-sign ] 4. [ + (-1) ] = [ - (+1) ] [ + (<->1) ] = [ <-> (+1) ] [ Negative-sign ] = [ Subtract-sign ] 5. [ Addition-sign ] = [ Positive-sign ] [ Negative-sign ] = [ Subtraction-sign ] 6. If, Definition [ + (-1) ] = [ {+(-1)} ] : Addition-sign -> Positive-sign [ - (+1) ] = [ {-(+1)} ] : Negative-sign -> Subtraction-sign [ - (-1) ] = [ {-(-1)} ] : Negative-sign -> Subtraction-sign [ + (+1) ] = [ {+(+1)} ] : Addition-sign -> Positive-sign [ {-(-1)} = { - (-1) } ] can be approved. 7. Law of Liuhui Brahmagupta [ N X (-N) ] = [ - ( N X N ) ] [ (-1) X (-1) ] = [ - { (-1) X 1 } ] = [ - { (-1) } ] = [ - (-1) ]

Negative times negative is positive. Negative number and Imaginary number http://www.flickr.com/photos/trapassing/3967573047/sizes/o/ http://www.flickr.com/photos/trapassing/3967573047/

If you (don't) have 4 lots of -5 you (don't) have -20. So multiplying a positive and a negative gives you a negative product. You might be able to get your and her head around the idea that not having (i.e. -) 4 lots of -5 is the same as actually having 20.