I can't seem to understand what they are..this is what the teacher explained us
N=Set of natural numbers
N*=??? I dunno....
Z=set of intergers...
Q= Set of rational number (Most complex one for the matter...)
All "numbers" fall under the category of complex numbers (C).
Within C, you also have categories for numbers which are either purely imaginary (I) or real (R).
All of R can be described as being either rational (Q) or irrational (examples: pi, euler's number, etc).
Q are numbers which can be described in terms of a fraction form: .
Example: 122 can be written as 122/1; 1.33... can be written as 4/3
Within Q, you can describe integers Z (all Q whose denominator is 1; examples: 12, 2, -456), natural numbers N (all positive integers excluding 0), and N* (all positive integers including 0).
These are just ways of describing numbers in analysis. For example, if an expression is described as being in N, you will be dealing with multiples of whole numbers (aka integers).
Some reading: Is zero a natural number?@Everything2.com
Counting from zero is not a natural thing to do. It takes a certain level of sophistication to realise that you can have a set containing zero elements, or that you need a number to describe such a set in the first place. As a result, most numeral systems from history (eg. Roman numerals) don't contain a symbol for zero, or any way to represent the concept. The most 'natural' way to count is by making a mark for every item counted.
However ...... in the Netherlands (for example) it's generally taught that the natural numbers are {0, 1, 2, ...}.
So probably the best thing to do is avoid the term 'natural' altogether and use the term 'positive' or 'non-negative' to specify unambiguously which set you're referring to in any given context.
So, as I set from the go get, the definition of N* is best got from the teacher that is using it.
Wolfram sez it best ...
Natural Number -- from Wolfram MathWorld