A mathematical proof is any mathematical argument which demonstrates the truth of a mathematical statement. Informal proofs are typically rendered in natural language and are held true by consensus; formal proofs are typically rendered symbolically and can be checked mechanically. "Proofs" can be valid or invalid; only the former kind constitutes actual proof, whereas the latter kind usually refers to a flawed attempt at proof.
Questions tagged [proof]
828 questions
0
votes
1 answer
Why peak1d won't miss a peak if it exists?
I saw the peak1d algorithm in here and on Peak finding algorithm.
I can't understand why it surely finds a peak if it exists. It seems that we are deciding to go with one half and can miss a peak on the other. I don't understand how comes you can…
0x90
- 39,472
- 36
- 165
- 245
0
votes
1 answer
Why does the formal procedure prove NP-Completeness?
I know how to show that a problem X is NP-Complete.
Show that X ∈ NP.
Show Y ≤p X: show a problem Y known to be NP-Complete can be reduced to X in polynomial time.
However, I'm stuck on why this procedure proves that X is NP-Complete. Could…
CocoaDog
- 305
- 1
- 11
0
votes
1 answer
Insufficiently evaluated context inside `with` clause
I'm stuck on the following proof.
module Temp where
open import Data.Empty
open import Data.Fin hiding (compare)
open import Data.Nat hiding (compare); open import Data.Nat.Properties
open import Function
open import Level
open…
Roly
- 2,126
- 2
- 20
- 34
0
votes
1 answer
issues in the proof of master theorem
I am reading the book CLRS(Introduction To Alglorithms , 3rd edition) , and find there seems to be a error in the proof of master theorem . In page 104 , in order to extend the proof to all integer, it use one inequation which seems to be incorrect.…
Chris.Huang
- 545
- 1
- 4
- 9
0
votes
4 answers
How to find the loop invariant and prove correctness?
int i, temp;
a is an array of integers [1...100]
i = 1;
while i < 100
if a[i] > a[i+1]
temp = a[i]
a[i] = a[i+1]
a[i+1] = temp
i = i+1
I'm having trouble understanding how to find loop invariants and writing…
atkayla
- 8,143
- 17
- 72
- 132
0
votes
3 answers
Prove ~s=>~p given (r=>s) and (p|q)=>(r|s)
I am trying to prove ~s=>~p (not s implies not p) given the following 2 premises.
r=>s [r implies s]
(p|q)=>(r|s) [(p or q) implies (r or s)]
I have tried several ways, trying to use OR elimination or Negation Introduction, but…
0
votes
2 answers
Proofing encog xor results in excel
I'm working to proof basic neural network results and so far haven't been able to. I'm doing a feed-forward xor problem in encog and export the final weights and calculated output.
To proof I just have an excel sheet where I input the weights,…
Israel
- 3
- 2
0
votes
2 answers
Algebra Help on Inductive Proof?
I am trying to learn inductive proofs for a test tomorrow. I am trying to understand a solution for a problem in a book, but my math is a bit rusty. Can somebody explain how these are all equal? I don't understand how the last equation was found…
danb
- 55
- 2
- 10
0
votes
1 answer
If we prove there is no starvation, we don't need to prove that there is no deadlock or livelock (progress)?
I googled Peterson algorithm proof and noticed that most sites don't bother proving the progress requirement, why is that? Can someone explain?
user2824983
- 53
- 1
- 7
0
votes
1 answer
What's the loop invariant for this code?
I need to come up with a loop invariant for a given piece of code:
//pre: x & y >= 0
//post: z = x^y
//computes pow(x, y), x^y
int pow(int x, int y){
int z = 1;
while(y > 0){
if(y%2==0){
y /= 2;
x = x*x;
…
ceptno
- 687
- 2
- 6
- 28
0
votes
1 answer
A different way to do induction on lists that needs a proof
I have defined an inductive definition of lists (called listkind) in order make it easy
for me to prove a specific theorem by induction on listkind rather than on list.
Inductive listkind {X}: list X -> Prop :=
| l_nil : listkind []
| l_one : forall…
larsr
- 5,447
- 19
- 38
0
votes
1 answer
Prove big O of addition and subtraction of functions
Suppose f(n) = O(s(n)) and g(n) = O(r(n)). Prove or disprove (by giving a counter example) the following claims:
f(n) - g(n) = O(s(n) - r(n))
if f(n) = O(g(n)), then f(n) + g(n) = O(s(n))
I really have no idea where to even start.. please lend a…
user2387902
- 47
- 2
- 6
0
votes
1 answer
Equality of two algorithms
Consider a tree of depth B (i.e.: all the paths have length B) whose nodes represent system states and edges represent actions.
Each action a in ActionSet has a gain and makes the system move from a state to another.
Performing the sequence of…
Eleanore
- 1,750
- 3
- 16
- 33
0
votes
1 answer
How to prove correctness of this algorithm?
I am solving a problem from codeforces.
Our job is to find a minimum cost to make a given integer sequence be a non-decreasing sequence. We can increase/decrease any number of the sequence by 1 at each step and it will cost 1.
For example, when we…
MS.Kim
- 219
- 2
- 4
0
votes
2 answers
Proving log(n!) is in Ω(n log(n))
The total cost of our operations are: Σ(i=1 to n) log(i).
Prove that this sum is Ω(n log(n)).
I'm a little bit stuck on how to go about proving this. I realize the summation comes out to be log(n!), since log(1) + log(2) + log(3) = log(3!) (and so…
user677786
- 455
- 1
- 6
- 13