Question

Part A: A circle is the set of all points that are the same distance from one given point. Find an example that contradicts this definition. How would you change the definition to make it more accurate? (5 points)
Part B: Give an example of an undefined term and how it relates to a circle. (5 points)

Answer 1

Answer:

A) this has a problem because does not explicit the dimension.

For example, the set {1, 3}

Is the set of all points that are at the same distance (1 unit) from the point x = 2.

If we write the definition as:

"A plane figure whose points are at a fixed distance to some given point, the center".

Then we are defining that is a "plane figure" so we need a plane to have a figure, so we need to have two dimensions, then there is no mistake in this definition.

B) The undefined terms are the terms without a definition, those are point, line, plane and set.

To have a circle we need a plane (because the circle "lives" in a plane) And the circle itself is the set of all the points that are equidistant to a point that is in that plane.

So we are using at least 3 of the undefined terms to define a circle.