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December 10th, 2017, 05:26 PM   #1
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Line Segment Arithmetic

Line Segment Arithmetic

Let all numbers be assigned an arbitrary collection of line segments equivalent in number to the number the line segments are assigned to: q = (q,q_)

Let zero be assigned one arbitrary line segment. (0,_)

0 = (0,_)
1= (1,_)
2= (2,_,_)
3= (3,_,_,_)

Let multiplication be defined as follows…

All binary operations of multiplication exist as a given number placed additionally into another given number’s number of line segments then added in all line segments.
(Any number in a binary expression of multiplication may be either the number or the number of line segments: but not both)

Let division by defined as follows…

All binary operations of multiplication exist as a given number placed equally and divisionally into another given number’s number of line segments then all numbers are subtracted in all line segments except one.
(In binary division the first given number must be the number, while the second number must be the quantity of line segments)


2 * 3 = 6
2 * 3_ = 6
(_,_,_) = 3 line segments
2 + 2 + 2 = 6
Or
2_ * 3 = 6
(_,_) = 2 line segments
3 + 3 = 6

a * 0_ = a = a * 0_
a_ * 0 = 0 = 0 * a_
0 * 0_ = 0 = 0_ * 0
a/0_ = a
0/a_ = 0
0/0_ = 0

a( b + c) = a * b+ a * c
a=1,b= 0,c=0
1( 0 + 0) = 1*0+1*0
1_* 0 = 1_*0+1_*0

For the distributive property to hold whatever is used as line segments of the lhs must be used as line segments on the rhs.

At no time may addition and subtraction be represented with a quantity of line segments

At no time may exponents and logarithms be represented with a quantity of line segments

At no time may a quantity of line segments be shown to be equivalent to anything or any number. It is only that a quantity of line segments is assigned to a number for the purpose of multiplication and division only.

Therefore, multiplication by zero is relative to zero used as a number or as a quantity of line segments

Therefore, division by zero is defined: n / 0_ = n

The quantity of line segments in zero may be expressed as the inverse of 1 only if it is assigned with a number.

0 is NOT the inverse of 1
1/0_ is the inverse of 1
1/0_ * 1/1_ = 1
1 *1_ = 1 = 0_ * 1 = 1
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