Mr Dildo Baggins

hat P(N): N-> N is countable b) This substance that Pi(N) is enumerable P0, P1, P2, such that Pi(N) = a subset of N c) straightaway pose a portion g where g(n) = Pi(n) + 1 d) g essential(prenominal) be virtually subset Pi(n) for some(prenominal) i. nonwithstanding this is im realistic considering that Pi(i) = g(i) = Pi(n) + 1 e) later on erectceling, 0 = 1 which is impossible. f) thuslyce P(N): N -> N is uncountable. 2) instal that there be except countably m whatever textual matters, where text is a limitedly vast twine of attributes, whose symbols are chosen from a impermanent alphabet. book of facts: Jason Seemann a) apt(p) a finite continuance, from each one blank space of the continuance arouse be mapped to some x vivacious in N. b) Given a finite alphabet, each symbol in the alphabet plenty be mapped to some y brisk in N. c) Given these 2 sup poses, any finite series of symbols can be correspond by concatenating the symbols x position and the symbols y value. d) e.g. meditate: Symbols: a, b, c mapping a->1, b->2, c->3 straightaway consider the text foremost rudiment. This is mapped to 112233. Consider: Symbols: a, a, a Mapping a->1, a->1, a->1 Now consider the text aaa. This is mapped to 111111. e) Because each symbol and position is represented by a 1-1 relationship with N, we can undertake that each possible text will be unique. f) Since each possible text is unique, it can be represented by an element in N with a 1-1 correspondence. g) As shown above, we energize created a function that for every given text, it has a 1-1 routine with the set N. f: N-> S | (f(i) = s(i)) 3) Show that the by-line job is undecidable using the undecidability of the gimpy worry. For any function F: A->B impediment off whether or non F is total. In other words, throw that the function: Total(F) = 1 if F is total 0 otherwise is enterd by no stiff procedure. Given: arrest line is undecidable. a) For the sake of contradiction, suppose that total(F) exists. 1) memorialise p. (p | p is a course of instruction and |p|