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Indexed Families of Sets

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Describe each of the following as an indexed family of sets. Here, pi denotes the coordinated xy-plane.

a) The family of closed intervals of length 1 on the real line.

b) The family of all circles in pi of radius 1 whose center is on the y-axis.

c) The family of all circles in pi of radius 1.

d) The family of all lines in pi with slope 6.

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Indexed Families of Sets are clearly emphasized.

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(a)
Define the real number , then an interval of length 1 is all the values of such that
The index of the set is the variable we can independently set and from it we can define the rest of the members of the set.
Here the variable is the initial point of the interval, r.
Hence, for ...

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