User blog comment:B1mb0w/Alpha Function/@comment-25337554-20150602103618/@comment-10262436-20150602111036

Hi. The Deeply Nested Ackerman function isn't well defined for real numbers. You could modify it, but you would need to take the integer parts of some real numbers when they are less than 1, to avoid infinite loops if the real numbers reduced below 0 and the function kept subtracting 1.

It is worth considering though.