What do the letters R, Q, N, and Z mean in math?

The letters R,Q,N,Z are the names of the set of the
numbers, that have specific properties.

For instance, N is
the letter which designates the set of natural numbers.

N =
{0 , 1 , 2 , 3 ,............. , n ,.............}

If the
set is N^*, that means that the 0 value does not belong to the set. We could also write
as:

N^* = N - {0}

The letter Z
designates the set of integer numbers, which contains positive and negative
elements.

Z = {... , -n ,.... ,-4 ,-3 ,-2 ,-1 ,0 ,1 ,2 ,3
,4 ,... ,n, .......}

So, the set Z is composed from the
elements of N and their opposed.

The conclusion would be
that N is a subset of Z.

Also Z^* =
Z-{0}.

The letter Q designates the set of rational numbers.
The set could be mathematically described as:

Q = {m/n / m
and n belong to Z, m is not divided by m}.

So, Q is
composed from elements, which are ratios, where the numerator is not divided by the
denominator and both, numerator and denominator, are
integer numbers.

The letter R designates the set of real
numbers. This set includes all the elements from the sets described above. So, we could
say that the sets N,Z,Q are the subsets of R.

In the set R
appear the symbols: -infinite and +infinite.

The set R is
described as an interval that is bounded by the symbols -infinite and +infinite. In this
interval, between the 2 boundaries, are located all the real
numbers.

R = (-infinite ,
+infinite)