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# irrational numbers

## summary

**irrational number**
*noun, Mathematics*
- (1) Any real number that cannot be expressed exactly as a ratio of two integers (excludes imaginary and complex numbers).
- (2) Any real number that is not a rational number.

Computers have limits on the largest and smallest irrational numbers that can be represented and rounding or approximation of irrational numbers.

### stub section

This subchapter is a stub section. It will be filled in with instructional material later. For now it serves the purpose of a place holder for the order of instruction.

Professors are invited to give feedback on both the proposed contents and the propsed order of this text book. Send commentary to Milo, PO Box 1361, Tustin, California, 92781, USA.

# irrational numbers

**irrational number**
*noun, Mathematics*
- (1) Any real number that cannot be expressed exactly as a ratio of two integers (excludes imaginary and complex numbers).
- (2) Any real number that is not a rational number.

Examples of irrational numbers include pi (π) Euler’s number (*e*), and the square root of 2 (√2).

The square roots of most (but not all) numbers are irrational. For example, √2, √3, √5, √6, √7, and √8 are irrational numbers, while √4 (which is 2) and √9 (which is 3) are both rational numbers.

Computers have limits on the largest and smallest irrational numbers that can be represented and rounding or approximation of irrational numbers.

The decimal expansion of an irrational number is an infinite series of digits that does not end in an infinite repeating sequence of digits.

# free music player coding example

**Coding example:** I am making heavily documented and explained open source code for a method to play music for free — almost any song, no subscription fees, no download costs, no advertisements, all completely legal. This is done by building a front-end to YouTube (which checks the copyright permissions for you).

**View music player in action:** www.musicinpublic.com/.

**Create your own copy** from the original source code/ (presented for learning programming).

Because I no longer have the computer and software to make PDFs, the book is available as an HTML file, which you can convert into a PDF.

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