Cut the Knot
Cut the Knot!: What Is a Number?
Casual and clear but definitely upper-level discussion of rational, real, imaginary, and several other types of numbers. Links to related sites.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Numbers
Math Forum response to request for information on various number sets. Also defined and discussed are integers, natural numbers, whole numbers, irrational numbers, transcendental numbers, and algebraic numbers.
Mathigon
Mathigon: Real, Irrational, Imaginary Numbers
Explore this course in imaginary and complex numbers including topics of integers, real numbers, infinity, transcendental numbers, imaginary and complex numbers.
Wikimedia
Wikipedia: Irrational Number
At this site from Wikipedia you can learn the definition of an irrational number, then look at examples and explanations of why some numbers are irrational and others are not.
University of Utah
University of Utah: The Number System
This site from The University of Utah provides a definition of commonly used numbers including rational numbers, natural numbers, integers, real and complex numbers and more.