#### questfortruth

##### Well-Known Member

Or maybe the number Pi cannot be expressed in terms of analytic functions but only in an infinite series. In such a case, what then is Pi called? Is there a special name for such numbers? What is the name of an irrational number that cannot be expressed through elementary functions? For example, Pi is not equal to the natural logarithm of a yet unknown rational number.

Suppose that exp(1)=ln(A). Is known that exp(1)=e is transcendental. But it is not known is A rational or irrational. If A is not rational, how e would be called? Super-transcendental?

Suppose that exp(1)=ln(A). Is known that exp(1)=e is transcendental. But it is not known is A rational or irrational. If A is not rational, how e would be called? Super-transcendental?

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