Is this how I should complete my proof:
By way of contradiction assume that 2k is the largest even integer.
Now consider (2k)!
(2k)! = (2k)(2k-1)(2k-2).......(k)(k-1)(k-2)......(2)(1)
= 2[k(2k-1)(2k-2).......(k)(k-1)(k-2)......(2)(1)]
= 2p, which is also an even integer. This contradicts...
The question was asking: Prove the following statement using either direct or contrapositive proof: If n is an integer then 4 does not divide n^2-3
Here is my working out:
let n^2 - 3 = 4m
By way of contradiction assume n^2 - 3 is rational, ie; n^2 - 3 = a/b (BTW in the funky looking...
I have come across some questions that are asking me to prove the general formula for a certain sequence. I do now know how to tackle these questions. Can someone please tell me how to do them?
Here is a problem from the question set that appeared:
A sequence is given by the first order...
For the following question when I am trying to prove the n = k+1 case am I allowed to substitute it in the first line of the question and also in the second line of the question?
What I am trying to say is am i allowed to assume:
I am really confused for the following proof question and am unsure where to start (I don't really get the hint)
I would really appreciate it if anyone helped me out with this question
I am just wondering if anyone can have a look at my solution to the following proof question:
Question: "Prove by contradiction that there exists no 'n' that is an element of the natural numbers, such that n^2 + 2 is divsible by 4"
My Solution:
By way of contradiction assume their exists...