__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= [(x_{1}– y_{1})^{2} + (x_{2}-y_{2})^{2}]^{1/2} where X=(x_{1}, x_{2}) and Y=(y_{1}, y_{2}).

__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 R_{c}(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.