Math 3334: Class Notes

Definition 1 – The statement that P is a point means P is an ordered number pair.

Defintion 2 – The statement that Q is the plane means Q is the set of all points.

Definition 3 – Suppose each of x and y is a point. The statement that D is the distance between x and y means D= [(x1– y1)2 + (x2-y2)2]1/2 where X=(x1, x2) and Y=(y1, y2).

Definition 4 – The statement that R is a region means there is a positive number c and a point P and R is the set to which x belongs, only in the case x is a point and D(x,p) < c. We may denote such a region by Rc(P).

Problem 1 – if each of R and S isa region adn there is a point P common to R and S, then tehre is a region T such taht P is in T and every point of T is in each of R and S.

Definition 5 – Suppose M is a point collection. The statement that P is a limit point of M means P is a point and if R is a region containing P, then tehre is apoint of M, distance from P, that belongs to R.

Problem 2 – Every point of a region R is a limit point of the region R.

Problem 3 – If R is a region and P is a point not in R, then P is not a limit point of R.

Problem 4 – If M is a number collection that contains the number 1 and if n belongs to M, then n+1 belongs to M, does M contain all positive integers?

Definition 6 – The statement that M is an infitie point collection means if N is a positive integer then M has N points.

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