A Calculus of Number Based on Spatial Forms - University of ...
A Calculus of Number Based on Spatial Forms - University of ...
A Calculus of Number Based on Spatial Forms - University of ...
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69<br />
A.2 Functi<strong>on</strong>s<br />
The standard algebraic functi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> additi<strong>on</strong>, subtracti<strong>on</strong>, multiplicati<strong>on</strong> and divisi<strong>on</strong><br />
can be formed with boundaries. Powers and transcendental functi<strong>on</strong>s can be formed<br />
with the same objects. These are shown below.<br />
Standard Boundary<br />
Identity x x<br />
Inverse ,x <br />
1=x ()<br />
Additi<strong>on</strong> x + y xy<br />
x , y x<br />
Multiplicati<strong>on</strong> x y ([x][y])<br />
x=y ([x])<br />
Power x y (([[x]][y]))<br />
x ,y<br />
yp x<br />
Transcendental e x (x)<br />
ln x [x]<br />
(([[x]][]))<br />
(([[x]]))<br />
A.3 <str<strong>on</strong>g>Number</str<strong>on</strong>g> Formats<br />
The boundary notati<strong>on</strong> does not restrict the structural format <str<strong>on</strong>g>of</str<strong>on</strong>g> numbers. The notati<strong>on</strong><br />
can express numbers in a variety <str<strong>on</strong>g>of</str<strong>on</strong>g> formats by adapting the algebraic structure<br />
<str<strong>on</strong>g>of</str<strong>on</strong>g> that format. Below are some examples.<br />
Dene b to be the base radix, b<br />
: = .<br />
Dene fAg to be the base boundary, fAg : =([b][A]):