exercise3
Exercise 1
Try to define a next function over 'I_n that correspond to the
successor function over the natural plus the special case that
n -1
is mapped to zero
Exercise 2
Show that injectivity is decidable for a function f : aT -> rT
with aT a finite
Exercise 3
Try to formalize the following problem
Given a parking where the boolean indicates if the slot is occupied or not
Number of cars at line i
Number of cars at column j
Show that if 0 < n there is always two lines, or two columns, or a column and a line
that have the same numbers of cars
Exercise 4
Prove the following state by induction and by following Gauss proof.
Exercise 5
Exercise 6
Exercise 7
Prove the following state by induction and by using a similar trick
as for Gauss noticing that n ^ 3 = n * (n ^ 2)
Exercise 8
building a monoid law