These are notations for number types, or number *groups*.

**N+** is the simplest group here. N is the group of all natural, or 'counting', numbers {0,1,2,3,...`infty ` }. Some people include 0 in this, others do not. So writing N+ makes it clear that 0 is *not* included, as + indicates 'positive', that is, *above zero.* So N+ is the group of all **positive natural numbers.**

**Q+** is the next simplest group here. Q is the group of all rational numbers {n1/n2} where n1 and n2 where n1 is an integer and n2 is a *positive *integer (NB, dividing by zero results in a singularity so n2 cannot be zero for numbers in this group, although n1 can). With the + again representing 'positive', Q+ is then the group of all **positive rational numbers.**

**R+** is the most complicated group here. R is the group of all real numbers, rational or irrational, so that it includes irrational numbers (with infinitely many numbers to the right of the decimal point) like *`pi ` * (= 3.14159......) and `e ` (= 2.71828......). As with the other groups above, the + indicates 'positive' so R+ is hence the group of all **positive real** **numbers.**