## Quick Reference

A finite interval on the real line is a subset of **R** defined in terms of end-points *a* and *b*. Since each end-point may or may not belong to the subset, there are four types of finite interval: *x* | *x* ∈ **R** and *a*≤*x*≤*b*}, denoted by [*a*, *b*],*x* | *x* ∈ **R** and *a* < *x* < *b*}, denoted by (*a*, *b*),*x* | *x* ∈ **R** and *a*≤*x* <*b*}, denoted by [*a*, *b*),*x* | *x* ∈ **R** and *a* < *x*≤*b*}, denoted by (*a*, *b*].There are also four types of infinite interval:*x* | *x* ∈ **R** and *a*≤*x*}, denoted by [*a*, ∞),*x* ∈ **R** and *a* < *x*}, denoted by (*a*, ∞),*x* | *x* ∈ **R** and *x*≤*a*}, denoted by (−∞, *a*],*x* | *x* ∈ **R** and *x* < *a*}, denoted by (∞, *a*).Here ∞ (read as ‘infinity’) and −∞ (read as ‘minus infinity’) are not, of course, real numbers, but the use of these symbols provides a convenient notation.

*x* | *x* ∈ **R** and *a*≤*x*≤*b*}, denoted by [*a*, *b*],

*x* | *x* ∈ **R** and *a* < *x* < *b*}, denoted by (*a*, *b*),

*x* | *x* ∈ **R** and *a*≤*x* <*b*}, denoted by [*a*, *b*),

*x* | *x* ∈ **R** and *a* < *x*≤*b*}, denoted by (*a*, *b*].

*x* | *x* ∈ **R** and *a*≤*x*}, denoted by [*a*, ∞),

*x* ∈ **R** and *a* < *x*}, denoted by (*a*, ∞),

*x* | *x* ∈ **R** and *x*≤*a*}, denoted by (−∞, *a*],

*x* | *x* ∈ **R** and *x* < *a*}, denoted by (∞, *a*).

If *I* is any of the intervals (i) to (iv), the open interval determined by I is (*a*, *b*); if *I* is (v) or (vi), it is (*a*, ∞) and, if *I* is (vii) or (viii), it is (−∞, *a*).

*Subjects:*
Mathematics.

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