Computability 1) Argue that the set of computer programs in any language must be at most countably infinite. What da 2) Argue that for a given programming language, most real numbers cannot be computed as the 3) Different programming languages have different abilities. Is it possible that between ProgrammingLan- we know about computer programs? (potentially infinite) output of any program. guage 1 and ProgrammingLanguage 2, they could, taken together, compute all real numbers? Why or why not. 4) Is it possible that the set of programming languages is uncountably infinite? Why or why not. Would it help us compute more things if it were? 5) Argue that there are functions from the natural numbers to the natural numbers that are uncomputable by any computer program. What do you need to show in order to prove this