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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Coq modular arithmetic
How do static analyzers prove overflow using Coq?
Do they have their own definitions of integers and not use the given sets?
Or does coq have an inbuilt type for n-bit integers and operations on them?
Prog
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Maximum independent set in a tree. Review algorithm, need proof
pseudocode:
void recursive('k'){ // 'k' and 'i' vertices
sumA = 0;
sumB = 0;
for each non visited 'i' neighbor do{
recursive('i');
sumA = sumA + b['i'];
sumB = sumB + max(a['i'], b['i']);
}
a['k'] = 1 + sumA;
b['k'] =…
sdadffdfd
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2 answers
Proving a function is in big theta using limit method
Hi I am faced with a problem of proving that a function is an element of big theta. The question reads as follows: is 4n^3+23n^2+1 (is an element of) Theta(n^3), and prove your answer. My answer is as follows:
Basically I am proving it is in both …
amine
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1 answer
Proof of induction on pseudocode
Given the pseudocode
MUL(a,b)
x=a
y=0
WHILE x>=b DO
x=x-b
y=y+1
IF x=0 THEN
RETURN(true)
ELSE
RETURN(false)
Let x(n) and y(n) denote the value of x and y after the while loop has run n times.
I have to show…
Labbiqa
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I can't understand of the RMS Scheduling proof
I'm Korean. Sorry to my awful English.
I was learned RMS Scheduling some days ago.
And, my professor explain these proof.
For example, there are two tasks
Proof
The second page that is 'Proof' is what I can't understand.
What is the T_n and…
Hyuntae Kim
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1 answer
Regular language closure under insertion
Suppose I have a regular language L under alphabet Σ. How do I show that the language L' is still a regular language when I insert a symbol in the middle?
For example, L includes a string w which consists of two substrings u and v (w = uv) I want to…
Darren B
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2 answers
All maximal independent sets of a matroid have the same cardinality
How to prove that all maximal independent sets of a matroid have the same cardinality.
Provided a matroid is a 2-tuple (M,J ) where M is a finite set and J is a
family of some of the subsets of M satisfying the following
properties:
If A is subset…
user3622539
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0
votes
1 answer
Complexity proof
I would to prove the following example:
n^k = O (c^n) for every k and c>1
It is noticeable that the polynomial function grows faster than exponential function. We try to find k0 > 0 satisfying the condition
fn > = k0 * g(n)
Than
n^k <= k0 *…
Ian
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Stable Matching Problem
I am currently reading an Algorithm's book and came across the Stable Matching Problem. And a question came to mind that I'm curious about, but the book doesn't answer.
In every SMP is it possible to always have one pair where each prefers the other…
user299648
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1 answer
Diameter of Connected subgraph with all nodes
Lemma 1:
If H is a subgraph of a graph G, then dist_G(u, v)<= dist_H(u, v).
Proof
Every u-v path in H appears also in G, and G may have additional u-v paths that are shorter than any u-v path in H.
Lemma 2:
If H is connected subgraph of a graph G,…
Manuel
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Binary search tree prove number of leaves
I have to prove that in binary search tree, number of nodes with two children is one less than number of leaves. I found some proofs by induction on the internet, but I wanted to approach this problem less 'mathematically'. So I thought of this:
-we…
Haratino
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Prove that all prefix sums are non negative
We have an array having n integers whose sum is non negative.
I need to prove that there exists an index i, such that starting from i, all prefix sums are non negative, till we reach i again circularly.
Say the array is a1, a2, a3, ..... , an, such…
sahil
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1 answer
Propositional Logic Formal Proof
I'm trying to formally prove the following equation, as practice ahead of my logic exam. However, I'm having a little difficulty working out the steps. Here are the rules that I'm using;
A ∧ A ≡ A, A ∨ A ≡ A idempotence
A ∧ B ≡ B ∧ A, A ∨ B ≡ B ∨ A…
user6066919
0
votes
2 answers
Show a complete graph with n vertices, the weight of a MST is less than or equal to the min weight of cycle that passes through all vertices
I am really struggling with this proof and would really appreciate a detailed explanation:
Show a complete graph with n vertices, the weight of a MST is less than or equal to the min weight of cycle that passes through all vertices (also called a…
Chad
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The number of connected (!) subgraphs is exponential?
i want to show that for an example graph family the nummer of connected subgraphs grows expnential with n.
That is easy to show for a complete graph, because a complete graph has
n(n-1)/2 = n over 2
edges. One edge is either in the subgraph or not.…
Perhalo
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