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Intervals as Subsets of R

Let a, b ∈ R and a < b. Then
  1. Open interval does not contain the endpoints. On the number line, open intervals (a, b) are defined as {x: a < x < b}.
 
  1. Closed interval includes its endpoints. On the number line, closed intervals [a, b] are defined as {x: a x b}.
  1. We can also have intervals closed at one end and open at the other,

[a, b) = {a : a ≤ x < b} is an open interval from a to b, including a but excluding b.

 
  1. (a, b] = {a : a < x ≤ b} is an open interval from a to b, excluding a but including b.
is called the length of any of the intervals





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