Ahhhh so it proves the hypothesis. I see now factorising was the way to do it. It's a lot more clear now thank you for the assistance. I really appreciate it.
Ohhh okay that makes a lot more sense. See the induction examples I find online aren't very helpful because they were just substituting n values.
I'm guessing now we would try to get both sides to be equivalent. So either by substituting a value for n that's greater than 0.
Or by just...
Hi again. I have one other problem I'm puzzled about.
(a) A sorting algorithm takes one operation to sort an array with one item in it.
Increasing the number of items in the array from n to n + 1 requires at most an
additional 2n + 1 operations. Prove by induction that the number of operations...
Hi, thanks for clearing that up, I really appreciate it.
So just to confirm, producing a counter statement would just be substituting values. E. G.
Let m = 9 and n=105. 105-9 =96 which is not big (>100) therefore the statement is irrational.
Hi I'm new here but can't get my head around this problem.
We use the predicates O and B, with domain the integers. O(n) is true if n is odd, and
B(n) is true if n if big, which here means that n > 100.
(a) Express ∀m, n ∈ Z|O(m) ∧ B(n) ⇒ B(n − m) in conversational English.
(b) Find a...