Fundamentals of Math

Fundamentals of Mathematics

Let's take a moment to unpack that statement, starting with "continuous quantity". To the average human most vales we interact with daily are rather fixed (e.g., $1.99, 20%, ¼ cup, ...), but numbers exists beyond these finite values. It is possible for a value to go on forever - like pi for instance.

≈ 3.141592653589793238462643383279502884197169399375105820974 …

Some continuous values may even form repeatable patterns.

1 3 ≈ 0.33333333333333333333333333333333333333333333333333333333 …

In essence, pretty much any number you can think of is a Real number, but because Real numbers contain so many types of numbers, we can further categorize them into parts to make them more discernible.

Figure 1.2.1 The Real Number System

Noting that the larger sets of numbers also include their small number counterparts. For example, by definition, we know -7 is an Integer it is also included in the set of Rational, Irrational, and Real Numbers.

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