precision – Göthel Software Blog

Natural numbers are defined as the sequence of numbers fully defined by their initial value, its successor and the successor of its successor and so forth. Despite the beauty of their intrinsic Dedekind–Peano axioms, they are also fully proven by induction.

${\begin{alignedat}{3}0&:=&&\quad \ \,\{\}&&=\emptyset \\1&:=0'&&=\{0\}&&=\{\emptyset \}\\2&:=1'&&=\{0,1\}&&=\{\emptyset ,\{\emptyset \}\}\\3&:=2'&&=\{0,1,2\}&&=\{\emptyset ,\{\emptyset \},\{\emptyset ,\{\emptyset \}\}\}\\&\vdots &&&&\\(n+1)&:=n'&&=\{0,1,\ldots ,n\}&&=n\cup \{n\}\end{alignedat}}$ Continue reading “Rational Expressions with frictionless Fractions and implemented Time” →