Class 11 Maths Sets Open & Closed Intervals

Open & Closed Intervals

Let a, b ∈ R and a < b.

Open interval is denoted by (a, b) = {x : a < y < b}. Endpoints element NOT included.

Closed interval is denoted by [ a, b ] = {x : a ≤ x ≤ b}. Endpoints element included.

We can also have intervals closed at one end and open at the other, i.e.,

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

Memory tip:

ONE (Open No endpoint).  

Open windows = Light

Closed Window = Dark

() Looks like O , so it is used for Open interval

[] looks like closed box, so it is used for closed interval

 

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