2.3 Representations of Numbers in Note M-6

The specifications of natural numbers, integers and the rational numbers in Note M-6 [RM99a] include the following representations:

• The natural numbers can be represented as

  d₁ :: d₂ :: ...:: d_n,

  where n >1, d_i e {0,1, ...9} for 1 < i < n.
• For integers we allow additionally the signs "+" and "-".
• Rational numbers can be an integers or a fraction (x/p), (-x/p), +(x/p), +(-x/p), -(x/p), and -(-x/p), where x is of sort Int and p is of sort Pos.

  For finite decimal fractions we allow also d₁ :: d₂ :: ...:: d_n ::: d'₁ :: d'₂ :: ...:: d'_m for the number d₁ d₂ ...d_n . d'₁ d'₂ ...d'_m and r E i for the number r * 10 ⁱ, where r is of sort Rat and i of sort Int.