Intervallum (mathematica)

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Intervallum vocatur copia inferior numerorum realium.

Genera intervallorum[recensere | fontem recensere]

Sunt haec intervalla:

  • Clausum:  [a,b] := \lbrace x \in \mathbb R: a \leq x \leq b \rbrace .
  • Apertum:  ]a,b[ \ := (a,b) := \lbrace x \in \mathbb R: a < x < b \rbrace .
  • Semi-apertum vel semi-clausum:
    1.  [a,b[ \ := [a,b) := \lbrace x \in \mathbb R: a \leq x < b \rbrace vel
    2.  ]a,b] := (a,b] := \lbrace x \in \mathbb R: a < x \leq b \rbrace .

Infinitas etiam more mathematicorum finis intervalli clausi admissa est:

  •  [a,\infty[ \ := [a,\infty) := \lbrace x \in \mathbb R: x \geq a \rbrace vel  ]a,\infty[ \ := (a,\infty) := \lbrace x \in \mathbb R: x > a \rbrace aut
  •  ]\infty,b] := (\infty,b] := \lbrace x \in \mathbb R: x \leq b \rbrace vel  ]\infty,b[ := (\infty,b) := \lbrace x \in \mathbb R: x < b \rbrace aut
  •  ]\infty,\infty[ \ := (\infty,\infty) := \mathbb R .

Conventione autem intervalla haec huius modi definiuntur:

  • Si  b>a valet, intervalla ea sunt vacua: [b,a] = (a,a) = [a,a) = (a,a] = \lbrace \rbrace = \emptyset
  • [a,a] = \lbrace a \rbrace .

Vide etiam[recensere | fontem recensere]