Number system: Draw a diagram representing the following....


Junior Member
Mar 12, 2006
On one of my homework problems it says to draw a DIAGRAM representing the following number systems: rational, real, natural, whole, integer, irrational. I know rational are those that can be written as the ratio of 2 integers but how do I diagram it? Also what are considered the natural?


Super Moderator
Staff member
Feb 4, 2004
At a guess, they're wanting you to draw the various types of numbers in terms of subset-hood.

All the numbers are real numbers, so draw a big circle (or oval, whatever), and label it "Real numbers".

The reals are split between the rationals (fractionals) and the irrationals. So split the circle in half, labelling halves appropriately.

Inside the rationals, you've got the integers (because numbers like "4" can also be written as "4/1", a fraction). So draw a (pretty large) circle inside the "rationals" half and label it.

Inside the integers, you've got the non-negative integers, which are (probably) the whole numbers. (Check your book's definition to see which of "whole" and "natural" includes the number zero.) Draw nested circles, and label.

I could be wrong, but I'd bet good money that the above is what they mean by a "diagram".