 The above result should not be confused with the common claim that computers can compute anything. This claim is false: another important result of computability theory is that most functions are not computable by TMs (and hence, by digital computers). TMs compute functions defined over denumerable domains, such as strings of letters from a finite alphabet. There are uncountably many such functions. But there are only countably many TMs; you can enumerate TMs by listing each TM specification (which is some finite string). Since an uncountable infinity is much larger than a countable one, it follows that TMs (and hence digital computers) can compute only a tiny portion of all functions (over denumerable domains, such as natural numbers or strings of letters).