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
How to prove StronglySorted list consing in coq?
I am trying to make a tower of Hanoi proof in Coq as a learning exercise. I am stuck with a last goal on my first proof after many hours of fruitless attempts.
Could you please explain why my program is failing, and how to correct it?
Edit: looking…
Raoul
- 1,872
- 3
- 26
- 48
0
votes
2 answers
Grouping 1-12 in groups of 4 with the least number of duplicates
Consider 12 people who want to meet up to play a game every week.
They meet in groups of 4. They want to play each other an even number of times.
After 4 weeks there doesn't seem to be any combination that allows each player to have played with all…
David Tong
- 91
- 11
0
votes
2 answers
Prove that a binary tree with n leaves has a height of at least log n
I know that the number of leaves in a binary tree of height h can be at most 2^h, and I also know how to prove this using induction. Where do I go from here?
I found this previously answered question, but this doesn't make any sense to me because I…
user928112
- 483
- 1
- 6
- 24
0
votes
1 answer
Coq - proving something which has already been defined?
Taking the very straightforward proof of "the sum of two naturals is odd if one of them is even and the other odd":
Require Import Arith.
Require Import Coq.omega.Omega.
Definition even (n: nat) := exists k, n = 2 * k.
Definition odd (n: nat) :=…
R. Rengold
- 193
- 13
0
votes
1 answer
SPF not working
Other people are using my domain to send emails. I am trying to protect it by setting up a SPF record. This is my SPF record: "v=spf1 -all"
However, look like it doesn't work. I have tried to send an email using PHP mail() function on another server…
Ty Trinh
- 37
- 6
0
votes
1 answer
Proving an upper bound to F(x)+G(x)
I have stumbled upon the following question:
If f(x),g(x) > 1 for every x, prove/disprove the following:
f(x)+g(x)= O(f(x)*g(x))
I dont know how to start the proof, this is very basic for my level, please help.
Eiad Amer
- 1
- 1
0
votes
1 answer
What is the loop invariant of the given program
I don't know how to find a loop invariant. I'm not sure where to start. Can anyone find the loop invariant of the given program and explain your method please.
{n ≥ 0 ∧ i = 0}
while i < n − 1 loop
b[i] := a[i + 1];
i:=i + 1
end loop
{∀j.(0 ≤ j < n −…
the_martian
- 632
- 1
- 9
- 21
0
votes
1 answer
Recurrence with logs T(n) = T(logn)+log(log(n))
How to find T(n)=Θ(f(n)) for the recurrence T(n) = T(logn)+log(log(n))?
I think T(n)= Θ(log(n)) but the proof is the hard part for me. I'm going to attempt to prove by substitution but please help me with that. I also tried a proof by induction…
Sudocode
- 69
- 2
- 10
0
votes
1 answer
Can every DFA be simulated by a PDA?
Given a Deterministic Finite Automata (DFA) M_1, does there always exist a Pushdown Automata (PDA) M_2 that accepts the same language as M_1? I.e. can any DFA be simulated by a PDA? Intuitively, it makes sense to me that a PDA is more powerful…
Paradox
- 4,602
- 12
- 44
- 88
0
votes
1 answer
Wilson Theorem in C++, incorrect output?
I have written a function that should check whether an integer is prime, using the Wilson theorem. However it outputs that 5 is not a prime number, which obviously is. I want to ask why is that?
#include
using namespace std;
long int…
A.Petrov
- 71
- 6
0
votes
1 answer
How to complete this proof of commutativity with `replace`?
On this documentation, it is mentioned how replace could be used to complete the proof, but it ends up using rewrite, which seems to be a syntax sugar that writes replace for you. I'm interested in understanding how to use it explicitly.
If I…
MaiaVictor
- 51,090
- 44
- 144
- 286
0
votes
1 answer
How to prove a SPARK.Text_IO procedure precondition will hold
I'm using SPARK.Text_IO from the spark_io example in SPARK Discovery 2017.
My problem is that many of the SPARK.Text_IO procedures have a precondition that I do not know how to begin to try to prove namely that the standard input is readable and…
LT 'syreal' Jones
- 97
- 1
- 9
0
votes
0 answers
Frama-c loop invariant
I just tried to prove a sort function in frama-c. However, when I proved the outer loop.
loop invariant 0 <= i \forall int a,b; 0<=b <=l-i-1 <=a < l ==>
t[a]>=t[b];
There is always with the orange bullets. I refer…
Haiyin
- 1
- 1
0
votes
2 answers
Determining Multiple of the Closest Pairs in Plane
When determining the closest pair of vertices in a plane with the sweep algorithm outlined below, is it possible to determine multiple pairs without additional runs?
Sort points according to their x-coordinates.
Split the set of points into two…
jbenett
- 1
0
votes
1 answer
Context free language (Pumping lemma a^n b^m c^min(n,m))
I'm struggling to solve the following problem. I'm supposed to use the pumping lemma.
To prove {a^n b^m c^min(n,m) | m,n >= 0 } is not Context Free.
user8891173