art with code

2012-02-04

More basic math

A couple more simple "why is that" breakdowns:

Why does multiplying by -1 give you the negative of a symbol:

(-1xA) = (-1xA)
(-1xA) = ((1xA) + -(1xA)) + (-1xA)
(-1xA) = A x (1 + -(1xA)/A + -1)
(-1xA) = A x (-(1xA)/A)
(-1xA) = -(1xA) x A/A
(-1xA) = -(1xA) x 1
(-1xA) = -(1xA)
(-1xA) = -A

Why is -(B x A) = (-B x A):

-(B x A) = -(B x A)

-(B x A) = -1 x (B x A) 
-(B x A) = (-1 x B) x A
-(B x A) = (-B x A)

Why does multiplying by 0 give you 0:

0A = 0A           | X + -X = 0
0A = (B + -B)A    | (X+Y)Z = XZ + YZ
0A = (BA) + (-BA) | (-BA) = -(BA)

0A = (BA) + -(BA) | X + -X = 0
0A = 0


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