Real numbers are an important part of mathematics, used to describe nearly all physical phenomena. A schematic diagram of the real number system can help to illustrate the structure of this set of numbers and the subsets contained within it.

The real number system is made up of all the numbers on a line from negative infinity to positive infinity. This includes all whole numbers (e.g. 1, 2, 3, etc.), all fractions (e.g. ½, ¾, etc.) and all irrational numbers (e.g. √2, π, etc.). It also includes any number that can be written as a decimal (e.g. 0.12345...).

Within this system are several subsets that we use in everyday life. The natural numbers (1, 2, 3, etc.) are those used to count or measure quantity. The integers (negative numbers, zero and positive numbers) are the numbers that make up our calendar days and years. The rational numbers (fractions and whole numbers) can be used to describe the size of objects, measure distances, and calculate proportions.

Lastly, the irrational numbers (those that cannot be written as a fraction or decimal) can be used to calculate circles and curved shapes, as well as describe properties of everyday objects. These numbers are necessary for providing accuracy to our measurements and calculations.

A schematic diagram of the real number system is useful for visualizing the various subsets contained within this set of numbers, and for gaining a deeper understanding of how these numbers are used in everyday life. By understanding and appreciating the structure of the real number system, we can better understand and utilize the powerful tools that mathematics provides us.

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