10 - Number Systems GapFill

In terms of number systems,   irrationalrationalrealnatural numbers, comprising non-negative whole numbers, are primarily used for   approximationhigh precisioncountingmeasuring.  A set containing all such numbers is typically denoted by a capital   RAIN, and such a set is   finiteemptyabstractinfinite.  A system of numbers that is identical, except that negative whole numbers also belong to it, is that of  integerimaginaryirrationalrational numbers.  A set containing all of these numbers is   finiteemptyinfiniteabstract, and would be denoted using a capital   INZR. 

In terms of numbers which permit digits after the decimal place, there are several types.    ImaginaryIrrationalRealRational numbers permit such precision, but such numbers must be expressible as a fraction.  So, one third is an example, as is the number '1', which could be written as the fraction ¹/₁.  The set of all such numbers is typically denoted with a capital   ITNQ.  Then there are   rationalirrationalrealimaginary numbers, none of which can be expressed as a fraction.  Both of these types of number fall under the umbrella term of   realordinalimaginarycomplete numbers, their set denoted with a capital   CTNR.