Numbers that decouple from the Integers

Numbers that decouple from the Integers

Take any number and ask if it can be converted to an integer using only the 4 basic operations: add, subtract, multiply, divide. If it can we say it's coupled to the integers. If not we say it's decoupled from the integers.

Clearly all rational numbers are coupled. So are many irrational numbers, for example sqrt(2) is irrational, but it's trivial to convert it to an integer.. sqrt(2)*sqrt(2)=2. Even many complex numbers are coupled, for example i*i=-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 abbottsystems@gmail.com