Friday, June 26, 2015

Limits – Intervals – Definition

Definition:
Let a, bR and a < b. Then the set {xR: a≤ x≤ b} is called a closed interval. 
It is denoted by [a, b]. Thus closed interval [a, b] = { xR: a ≤ x ≤ b}. It is geometrically represented by 



  
Open interval (a,b) = {x∈R: a < x < b}. It is geometrically represented by



   
Left open interval (a, b] = {x∈R: a < x ≤ b}. It is geometrically represented by


    

Right open interval [a, b) = {x∈R: a ≤ x < b}. It is geometrically represented by



 
[a,∞) = {x∈R : x ≥ a} = {x∈ R : a ≤ x < ∞} It is geometrically represented by




(a, ∞) = {x∈R : x > a} = {x∈R : a < x < ∞}




(−∞, a] = {x∈R : x ≤ a} = {x∈ R : −∞ < x < a}



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