Undefined terms: What are they?

Recall that we have discussed about the meaning of “undefined” in different contexts.  In this post we are going  to discuss the meaning of undefined terms. What do we really mean when we say undefined terms in mathematics?

Polygons (via Wikipedia)

The time we started to learn mathematics, we also started to learn its vocabulary. We have learned about the definitions of terms such as triangles, fractions, polynomials, axioms, etc.  In our years of studies, we also have acquired the skill of being concise and precise in what we say or write.  Like in other fields of endeavors, we need to understand each other and make sure that we mean the same thing when we say a particular word. That is why we need to define them.  For example, when we say p0lygon (see figure above), we mean (loosely) that it is a plane figure bounded  by a finite number of line segments. Notice that from the definition itself, we must also define the other terms used. What do we mean by plane figure or line segment? » Read more