Top "Proof" questions

A mathematical proof is any mathematical argument which demonstrates the truth of a mathematical statement.

What is the proof of of (N–1) + (N–2) + (N–3) + ... + 1= N*(N–1)/2

I got this formula from a data structure book in the bubble sort algorithm. I know that we are (n-1) * (…

formula proof
What is the Pumping Lemma in Layman's terms?

I saw this question, and was curious as to what the pumping lemma was (Wikipedia didn't help much). I understand …

theory proof pumping-lemma
I need help proving that if f(n) = O(g(n)) implies 2^(f(n)) = O(2^g(n)))

In a previous problem, I showed (hopefully correctly) that f(n) = O(g(n)) implies lg(f(n)) = O(lg(…

big-o logarithm proof
How to determine the height of a recursion tree from a recurrence relation?

How does one go about determining the height of a recursion tree, built when dealing with recurrence run-times? How does …

recursion tree computer-science recurrence proof
Boolean Algebra - Proving Demorgan's Law

I looked all over Google for a boolean algebra (not set theory) proof of DeMorgan's Law, and couldn't find one. …

boolean-logic proof demorgans-law
Using big-O to prove N^2 is O(2^N)

I can clearly see than N^2 is bounded by c2^N, but how do i prove it by using formal …

big-o proof
Proof that the halting problem is NP-hard?

In this answer to a question about the definitions of NP, NP-hard, and NP-complete, Jason makes the claim that The …

theory proof halting-problem np
Number of binary search trees over n distinct elements

How many binary search trees can be constructed from n distinct elements? And how can we find a mathematically proved …

algorithm math binary-tree binary-search-tree proof
Explain the proof by Vinay Deolalikar that P != NP

Recently there has been a paper floating around by Vinay Deolalikar at HP Labs which claims to have proved that …

math computer-science complexity-theory proof p-np
Writing a proof for an algorithm

I am trying to compare 2 algorithms. I thought I may try and write a proof for them. (My math sucks, …

algorithm proof proof-of-correctness