>> 
No. 4413
Anonymous
28th May 2018 Monday 7:41 pm
4413
>>4412
Logically, what is a 'problem'? We can conceive of solving a problem as deciding whether a string belongs to a specified set of strings.
Solving the problem 'is 6 is even?' means deciding whether '6' belongs to the set {'0', '2', '4', '6', '8', ...}.
A computer program can be expressed as a string of text but not all strings are computer programs. So the set of all possible computer programs is smaller than the set of all possible strings.
By the power set rule, the set of all possible sets of strings is greater than the set of all possible strings.
Therefore, there are more problems than programs to solve them.
programs = strings
problems = sets of strings
