Probably the most common diagram is the number line.
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"Examples of schematic diagram of the real number system?"
An irrational number is included in the Venn diagram of real numbers. The subsets of the set of the real numbers are: The set of all natural numbers, N; the set of all whole numbers, W; the set of all integers, I; the set of all rational numbers, Q; and the set of all irrational numbers, S. It is obvious that N is a subset of W, W is a subset of I, and I is a subset of Q, but similar relationship doesn't hold between Q and S. However, this fact does not mean that irrational numbers are not in the Venn diagram, because they are also real numbers as well.
real numbers
False. Irrational numbers are real numbers.
rational numbers and irrational numbers