By popular demand, I’m posting a Venn Diagram illustrating the relationship between the commonly-named subsets of real numbers:
The two rectangles are merely labels for the similarly shaded parts of the ovals. So the two green sections are the irrational numbers, and the gridded section is the transcendental numbers. Irrational could be defined as “not rational” and transcendental could be defined as “not algebraic”. If anybody knows of a clearer way to venn-diagram these sets, I’d be interested to see it.
Note that as far as infinite cardinalities go, the six terms fall into two different sizes: Integers, Rationals and Algebraic numbers are the same size, and are each smaller than the Irrationals, Transcendentals, and Reals, which are the same size as each other.
Remind me to write a post about how there are as many points on an inch-long line segment as there are in the entire universe.