The Venn Diagram on Different Type of Numbers

Venn diagram show relations among several sets.

Natural numbers, Integers, Rationals and Real numbers each define a set. Therefore, they can be represented by the Venn diagram.

Can we draw the diagram in such a way that the area of each circle is proportion to how many numbers are in the set represented by the circle (or whatever shape)? And first things first shall we try that?

Now let’s elaborate.

Natural numbers (or counting numbers) are like 1, 2, 3, .. We use them when counting.
Integers include all natural numbers as well as zero (0) and all negative numbers like -1, -2, -3, ..

Rational numbers are those that can be written as the ratio of two integers. Rational numbers includes integers; rational numbers can be either positive or negative.
Examples are like 1 &frac; 2 or 2 &frac; 3.

What’s the real numbers? Well, they includes both Rational and Irrational numbers. Irrational numbers are those that CANNOT be written EXACTLY as the ratio of two integers. Two famous examples are sqrt(2) as well as π. Indeed, as learning more, we find much more IRRATIONALS than RATIONALS — so that if we resize total REAL numbers to 100, then 100% will be IRRATIONAL, and ALMOST NOTHING is RATIONAL.

In Venn diagram, we typically represent one set by a circle. Two circles overlap indicates they have common elements. If one circle is completely contained in another circle, that indicates one set A is completely contained in another set B (that is, any element of set A is an element of set B).


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