Math 151 Solutions to selected homework problems Section 1.2
... Show that aZ ∩ bZ = [a, b]Z. Solution: Let x ∈ aZ ∩ bZ. Then x ∈ aZ and x ∈ bZ, i.e. x is a multiple of both a and b. By definition of lcm, x is a multiple of [a, b]. Therefore x ∈ [a, b]Z. Thus we have aZ ∩ bZ ⊆ [a, b]Z. Now let x ∈ [a, b]Z. Then x is a multiple of [a, b]. It follows that x is a mu ...
... Show that aZ ∩ bZ = [a, b]Z. Solution: Let x ∈ aZ ∩ bZ. Then x ∈ aZ and x ∈ bZ, i.e. x is a multiple of both a and b. By definition of lcm, x is a multiple of [a, b]. Therefore x ∈ [a, b]Z. Thus we have aZ ∩ bZ ⊆ [a, b]Z. Now let x ∈ [a, b]Z. Then x is a multiple of [a, b]. It follows that x is a mu ...
Problem 1 - IDA.LiU.se
... Problem 4 ------------------------------------------------------------------------------------------------------------------Write a procedure (repeated start times fn) which applies fn on itself times times, beginning with start as the “initial” argument. > (define inc (lambda (number) (+ number 1)) ...
... Problem 4 ------------------------------------------------------------------------------------------------------------------Write a procedure (repeated start times fn) which applies fn on itself times times, beginning with start as the “initial” argument. > (define inc (lambda (number) (+ number 1)) ...
7 - blacksacademy.net
... above [1.6] that it was impossible that such a machine could exist. But let us pretend that BB exists and try to design it. Then it would compute p n by starting off by scanning the leftmost of a string of n 1 1s on an otherwise blank tape. From thence it must construct every Turing machine of ...
... above [1.6] that it was impossible that such a machine could exist. But let us pretend that BB exists and try to design it. Then it would compute p n by starting off by scanning the leftmost of a string of n 1 1s on an otherwise blank tape. From thence it must construct every Turing machine of ...
List comprehensions - MIT OpenCourseWare
... Part 1: Even Squares Define a procedure, called evenSquares that takes a list of numbers as input and returns a list of the squares of the input values that are even. Use a list comprehension. You can test whether a number is even by seeing if the number mod 2 is 0, that is, x % 2 == 0 ...
... Part 1: Even Squares Define a procedure, called evenSquares that takes a list of numbers as input and returns a list of the squares of the input values that are even. Use a list comprehension. You can test whether a number is even by seeing if the number mod 2 is 0, that is, x % 2 == 0 ...