Replace Numbers with Sets in calculations (1).

Replace Numbers with Sets in calculations (1).

Why it’s so important to calculate with sets ?

  • Some calculations are not defined with numbers but have a result with sets :
    • \frac{\lbrace 3 \rbrace}{\lbrace 0 \rbrace}=\emptyset
    • et \frac{\lbrace 0 \rbrace}{\lbrace 0 \rbrace}=\mathcal{P}(\mathbb{N}),\mathcal{P}(\mathbb{Z}),\mathcal{P}(\mathbb{D}), \mathcal{P}(\mathbb{Q}), \mathcal{P}(\mathbb{R}), \mathcal{P}(\mathbb{C}), ... depending on which set, the operation / is difined.
  • Computer Operating Systems return an error for such calculations. Thus we could think that consequences are similar. But interpretations are very different.
    • No results in the first case.
    • Many results or an infinity of results in the second case, a really tricky case to interpret, depending of the set, calculus accuracy, ... :
      • calculus accuracy,
      • set nature,
      • ...
  • The use of Set Calcul would force to evaluate more interpretations.