I'm a bit confused by the formatting but I think this is what you want:
natural numbers: [1,infinity], no commas
whole numbers: [0,infinity], no commas
integers: [-infinity,+infinity], no commas
rational numbers: every real number which can be written as a/b -> [-infinity,+infinity], with commas
irrational numbers: every real number which can't be written as a/b -> ones with infinite non repeating comma digits
0: whole number (-> also integer and rational)
-10^2=100=natural number (-> also whole number, integer and rational)
1.35=135/100=rational number
-90=integer (->also rational)
2/0=undefined...so not any kind of number
30^2=natural number (-> also whole number, integer and rational)
-1=integer (-> also rational number)
5.222...=5+2/9=47/9=rational number (don't get confused by repeating sequences of numbers, they are not irrational)
