 Let's look now at nested definitions. This is just like nested sets. Like the natural numbers are a subset of the integers, which are a subset of the rational numbers, which are a subset of the real numbers. It's better in this Venn diagram. Every natural number is an integer. Every integer is a rational number, and every rational number is a real number. Let us use that nested scheme to define a square. We need to start somewhere, so let us say that a figure is that, which is contained by a boundary. This is very similar to the definition that Euclid gives in his elements. So a polygon is a figure whose boundaries are line segments. A quadrilateral is a polygon with four sides. A parallelogram is a quadrilateral whose opposite sides are parallel. A rectangle is a parallelogram whose interior angles are right. A square is a rectangle whose sides are equal. Hence, we can see that every square is a rectangle, but not every rectangle is a square. Using the Venn diagram, this is what we have. Every square is a rectangle, every rectangle is a parallelogram, every parallelogram is a quadrilateral, every quadrilateral is a polygon, and every polygon is a figure. Thank you.