Just noticed the name of this thread. Blonde moment.
Gonna point out bits and pieces as I go through. Cuz I don't have time to go through it all in one sitting and if you waited for me to do that, you might never get my 2c. :p
1. You have an interesting definition of rational numbers. I personally would have favoured a definition that was more along the lines of "a rational number is any number that can be expressed as the fraction m/n of two integers, a non-zero denominator n and a numerator m." Because your definition sounds like you're saying 1.5 and stuff like that isn't a rational number when I'm fairly sure it is.
2. Similarly, I think your definition of irrational numbers needs to be reworked. It's a tad ambiguous.
3. At one stage you say: "Not an element of [symbol]". I think that needs to be changed to "[symbol] may be used to denote an item is not an element of..." Because I feel like it might be a bit ambiguous to someone who has no idea what you're talking about.
4. Your explanation for union needs more detail/specificity methinks. Despite doing well-ish in methods and unofficially tutoring other kids this year, I still don't know what you meant...
That's all for now.