Intervallum (mathematica)

Intervallum vocatur copia inferior numerorum realium.

Genera intervallorum

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: $[b,a] = (a,a) = [a,a) = (a,a] = \lbrace \rbrace = \emptyset$
• $[a,a] = \lbrace a \rbrace .$

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