What other mathematical sets are there apart from R?

Question

i.e. R for real numbers

Answer 1

there are the complex number, which is another field.
there are the quaternion numbers, but these do not form a field (the multiplication is not commutative).
and finally
there are the octonions, but these are not distributive.

but the amazing thing is, that these are all...
no more!!!!!.

Answer 2

Other mathematics sets include:

N: Natural Numbers {1,2,3,4, ....}
W: Whole numbers {0,1,2,3,4, ....}
I or Z: Integers {.....-3,-2,-1,0,1,2,3,....}
Q: Rational Numbers {a/b, where b is not equal to 0 and a and b are both integers}
The set of irrational numbers (numbers that neither terminate nor repeat, i.e. PI, e, sqrt(2), and so forth). I can't remember what letter they're denoted by

As a side note, real numbers are defined to be the combined set of all rational and irrational numbers.

Notice that some sets include others; the set of whole numbers, for instance is just 0 with the natural numbers, and the set of integers just includes the negative values. Also note that all the integers can be expressed as themselves over 1, so they're rational numbers.