[FOM] Query on real functions

[William Tait]

At 5:19 PM -0400 10/14/03, JoeShipman at aol.com wrote:
>Can anyone identify a real-valued function f continuous on [1, 
>infinity) with the following two properties:
>
>1) f eventually dominates any function in the sequence e^x, e^(e^x), 
>e^(e^(e^x)), ....
>
>2) f is defined in some other way than by defining it first at all 
>integers and then interpolating
>

If 2) could be replaced by some positive condition you need 
satisfied, it might help.

Bill