 Exercises from the text "Foundations of Analysis" by Joseph L. Taylor.

7.2 [ 12*, 13*, 16 ]
 7.3 [ 1, 2 ]
 Additional exercises.
A* 
Let a, b and c be real numbers such that a^{2} + b^{2} = 1. Let
£ = { (x,y) ∈ R^{2}: ax + by = c}
be the points on a line in the plane. Show that £ is a closed set.

 
B* 
Let S=∪_{n=1}^{∞}{x_{n}} be the set in R^{2} consisting of points from the sequence x_{n}=( 1/n, 1/n ). Determine whether S is open, closed or neither. Prove your answer.

