An irrational number is a real number that cannot be expressed as a ratio of integers.
Is it possible to formulate a "positive" definition for irrational numbers?
A few examples:
- An irrational number is a real number that can be expressed as…
- An irrational number is a real number that can be expressed only as…
I cannot find any such definition which does not include the term irrational number to begin with.
Since not all irrational numbers are computable, I believe that the answer is No.
Any idea how to prove it formally?
Thanks
Best Answer
An irrational number is a real number that can be expressed as an infinite simple continued fraction.