In mathematics and science, what do the notation Q+ ,N+,R+ refer to?

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mathsworkmusic | (Level 2) Educator

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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.

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