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Transcendental Numbers - A Simple Definition

Transcendental Numbers - A Simple Definition

Take any number and ask if it can be converted to a rational number by raising it to an positive integer power. If it can we say it's coupled to the integers. If not we say it's decoupled from the integers.

All rational numbers are coupled by definition. But so are many irrational numbers, for example sqrt(2) is irrational, but (sqrt(2))^2=2. Even many complex numbers are coupled, for example i^2=-1

So it seems most numbers are coupled to the integers, making integers fundamental. Not true. In fact Cantor showed the opposite is true, most numbers are decoupled from the integers. These are the (still mysterious) transcendental numbers. And the name is good, transcendental numbers "transcend" the integers.

Content written and posted by Ken Abbott