Vorlesung 2 Grüning

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Absolute Unlösbarkeit

Seite 7

(define f
  (lambda (n)
    (if (= n 1)
        1
        (if (even? n)
            (+ (f (/ n 2)) 1)
            (/ 1 (f (- n 1)))
            )
        )
    )
  )

(f 1)

(define f^-
  (lambda (n)
    (if (= n 1)
        1
        (if (> n 1)
            (* (f^- (- n 1)) 2)
            (+ (f^- (/ 1 n)) 1)
            )
        )
    )
  )

(f^- 1)

Überabzählbar unendlich

Seite 11

\table

Hilbert Hotel

(define stream-car car)

(define stream-cdr
  (lambda (stm)
    (force (cdr stm))))

(define-macro (stream-cons head tail)
  `(cons ,head (delay ,tail)))

(define stream?
  (lambda (stm)
    (and (pair? stm) (promise? (cdr stm)))))

(define stream-map
  (lambda (proz stm)
    (stream-cons (proz (stream-car stm)) (stream-map proz (stream-cdr stm)))))

(define show-stream
  (lambda (stm n)
    (letrec
        ([show
          (lambda (stm n ls)
            (if (= n 0)
                (apply display (append ls (list "...")))
                (show (stream-cdr stm) (- n 1) (append ls (list (stream-car stm) ", ")))))])
      (show stm n ()))))

(define zeige-mir show-stream)

(define baue-hilberthotel
  (lambda ()
    (stream-cons #f (baue-hilberthotel)))
  )

(define hilberthotel (baue-hilberthotel))

(zeige-mir hilberthotel 11)

(define einzelbuchung
  (lambda (val stm pos)
    (let ([old-pos pos])
      (letrec
          ([shorten
            (lambda (val stm pos)
              (if (= pos 0)
                  (if (eq? #f (stream-car stm))
                      (stream-cons val (stream-cdr stm))
                      (raise (string-append (number->string old-pos) " schon belegt mit: " (stream-car stm))))
                  (stream-cons (stream-car stm) (shorten val (stream-cdr stm) (- pos 1)))
                  ))
            ])
        (shorten val stm pos)
        )
      )
    )
  )

(set! hilberthotel (einzelbuchung "Otto Grundmann" hilberthotel 3))
(zeig-mir hilberthotel 12)

(define baue-kleinbus
  (lambda (numb pers)
    (list numb pers)))


(define kleinbus815 (baue-kleinbus 815 8))

(zeig-mir kleinbus815)

(define kleingruppenbuchung
  (lambda (hotel finite-bus)
    (letrec
        ([helper
          (lambda (hotel finite-bus pos)
            (if (not (empty? finite-bus))
                (helper (einzelbuchung (car finite-bus) hotel pos) (+ pos 1))
                (hotel)
                )
            )
          ])
      (hotel finite-bus 0)
      )
    )
  )

(set! hilberthotel (kleingruppenbuchung kleinbus815 hilberthotel))

(zeig-mir hilberthotel 12)

Vorlesung 2 Grüning

Absolute Unlösbarkeit

Überabzählbar unendlich

Hilbert Hotel

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