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
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Minimal Spanning Tree allowing equal edges but each cycle in the Graph contains distinct edges
I need to prove that there exists only one Minimum Spanning Tree that allows the graph to have equal edges. If there are any cycles in the Graph, the edges in each cycle has distinct weights. We have to prove it assuming the Minimum Spanning Tree is…
Spencer Fronberg
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1 answer
Prooving by induction that a function gets called n-1 times
This is the pseudo-code from the problem:
Procedure Foo(A,f,L), precondition:
A[f..L] is an array of integers
f,L, are two naturals >=1 with f<=L.
Code
procedure Foo(A,f,L
if (f=L) then
return A[f]
else
m <-- [(f+L)/2]
…
user8735013
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2 answers
Proving Big Omega Function
I'm trying to find the n0 (n not) of a function with a big omega size of n^3 where c=2.25
() = 3^3 − 39^2 + 360 + 20. In order to prove that () is Ω(^3), we need constants , 0 > 0 such that () ≥ ^3 for every ≥ 0
If c=2.25, how do I find the…
chrisd1120
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solving the recurrance by the method of substitution
While learning the algorithms and referring to CLRS, I came across a problem
T(n) = T(n-a) + T(a) + cn ; a >= 1 and c > 0
it is Big-theta(n^2), can be easily proved by recursion tree method
I can solve it by the method of recursion tree.
While…
Adorn
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Algorithm time complexity using recurrence relations
I have two questions about analyzing time complexity using recurrence relations.
Question 1. How to form recurrence relations for an algorithm when using memoization? Is this even possible?
For example consider computing the nth term of the…
Arat254
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Understanding the meaning of CheckHalt(X,X) in the proof of a theorem in Sussana Epp's Discrete Mathematics with applications
I have a very basic exposure to algorithms. I am a graduate in Mathematics. I was reading Halting Problem in the book Discrete Mathematics with applicationbs by Susanna Epp. It has a following theorem :
Theorem : There is no computer algorithm…
Error 404
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How many times does this recursive function iterate?
I have a recursive function, as follows, where b >= 0
def multiply(a,b):
if b == 0:
return 0
elif b % 2 == 0:
return multiply(2*a, b/2)
else:
return a + multiply(a, b-1)
I would like to know how many times the…
alexcons
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Give the Mathematical Proof of the Square Root finding algorithm
Can anyone explain the mathematical correctness of the following code to find the square root of a positive number in C++ ?
#include
#include
using namespace std;
int main(){
float a; cin>>a;
cout<<"Answer by Math…
Aayush Chaturvedi
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Structural induction proof on filter infix on filter
I am trying to prove the following:
filter p . filter q = filter (and p q)
where
and p q x = p x && q x
here is my try, but i am not sure if it is correct, can anyone give me some ideas?
Induction of list xs
Base case xs = []
(filter p . filter…
Edison Lo
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2 answers
Proof involving unfolding two recursive functions in COQ
I've began learning Coq, and am trying to prove something that seems fairly simple: if a list contains x, then the number of instances of x in that list will be > 0.
I've defined the contains and count functions as follows:
Fixpoint contains (n:…
LogicChains
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Geometric proof of Convergence of Perceptron Algorithm
I have a question considering Geoffrey Hinton's proof of convergence of the perceptron algorithm: Lecture Slides.
On slide 23 it says:
Every time the perceptron makes a mistake, the squared distance to all of these generously feasible weight…
R. Downey
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How to prove this using the formal definition of big-O?
I would like to prove that n^1000000 = O(1.000001^n) using the formal definition of big-O. I was wondering if I could do this using a proof by induction or a proof by contradiction. I would also like to do this without using limits.
Raven
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Pretty Printing Scala Case Classes Like A Tree
I am looking to build a tool that when an expression is input into it, it would produce a step by step evaluation proof and render it as a tree. I will also do the same thing for type checking tree.
Here are several examples of expressions and their…
StudentOfLogic
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Proving the Big-Theta and other asymptotic definitions (Big-Theta, Big-Omega, Big-O, little-theta, little-omega)
So in a future assignment, I noticed some problems that requested us to just "use" these rules. I was wondering if any rules existed for little-theta, and little-omega as well (using limit as x approaches infinity of f(x)/g(x)).
Also, are there any…
Raymond Zheng
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1 answer
All pairs out of four
This is a problem that's bugging me and I can't seem to unravel it.
A friend mentioned that they do a trip over Christmas week each year. They have a family of four and they rotate, each pair planning the vacation in secret that year and surprising…
Thom
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