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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3 answers
How can I prove by induction that the second of these two algorithms is faster?
I have two algorithms.
A. Solves problem in 2^n seconds.
B. Solves problem in n^2 + 1,000,000 seconds.
How can I inductively prove that B is faster than A.
I'm told that 2^n > 2n+1 for n>2 might be useful for this problem. I've been cracking my…
amorimluc
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How can I prove the following logic statement deductively?
I have the following logic statement:
If (P OR Q) and
(P => Q) and
(Q => P)
Then
(P AND Q)
I'm told to use Dorothy's Law, which is:
If (A => B)
Then (A OR B => B)
I can't figure out the exact rules of inference and/or laws needed to…
amorimluc
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votes
1 answer
compress 2-bit numbers and save 1 bit use compression scheme
I want to create a compression scheme for 2-bit numbers such that it will reduce the size of any sequence by at least one bit. How can I prove this is not possible?
benji_r
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2 answers
Proving an algorithm's correctness in determining the number of 1 bits in a bit string
procedure bit count(S: bit string)
count := 0
while S != 0
count := count + 1
S := S ∧ (S − 1)
return count {count is the number of 1s in S}
Here S-1 is the bit string obtained by changing the rightmost 1 bit of S to a 0…
John Taylor
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1 answer
Lambda calculus in practice
How to choose a language, a lambda term (λx.y)((λx.xxx)(λx.xxx)) actually calculated? In other words, need a language to the normal order reduction and the weak type system.
ramntry
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Proof on less than and less or equal on nat
Assuming the following definitions (the first two are taken from http://www.cis.upenn.edu/~bcpierce/sf/Basics.html):
Fixpoint beq_nat (n m : nat) : bool :=
match n with
| O => match m with
| O => true
| S m' => false
…
huynhjl
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votes
1 answer
Prove binary tree properties using induction
I am having trouble proving binary tree properties using induction:
Property 1 - A tree with N internal nodes has a maximum height of N+1
base case - 0 internal nodes has a height of 0
assume - a tree with k internal nodes has a maximum…
Zach Caudle
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votes
4 answers
How would one know if one saw a random number generator?
I have been reading various articles about random numbers and their generators. There are usually 3 important conclusions that I draw from them:
Random numbers are not truly random
Much of the time they have a bias (modulo bias)
Humans are…
mjgpy3
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1 answer
Proving lemma with implication based on functions
I want to prove the lemma below. I am trying to to use tactic 'destruct', but I
can't prove it. Please any body guide me how can I prove such lemmas. I can prove it for EmptyString, but not for variables s1 and s2. Thanks
Inductive nat :…
Khan
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1 answer
Proof with big-oh
Just starting to learn big-oh and asymptotic analysis and I am stuck on this particular proof:
How can we prove 2^n is O(n!)?
Thanks
user1421195
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-1
votes
1 answer
Prove (p → ¬ q) → ¬ (p ∧ q) in Lean4
I get as far as this
theorem problem_2 : (p → ¬ q) → ¬ (p ∧ q) := by
intro hp
intro hpw
which gets me to ⊢ False
helpoatmeal
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- 4
-1
votes
2 answers
Algorithm to sort an Array, in which every element is 10 positions away from where it should be
What is the most efficient sorting algorithm to sort an Array, that has n elements and EVERY element originally is 10 position away from its position after sorting?
I am thinking about insertion sort, but I have no clue how to proof that:
(1) It is…
El magnifico
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- 5
-1
votes
1 answer
Coq begginer here, how to understand the syntax?
I recently started a class on my college where we solve logical problems in Coq. I'm having problems understanding the principles of programming in Coq, the syntax and "building" ideas in my brain when it comes to problems. For instance,
Definition…
SD01
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-1
votes
2 answers
Show that the class of decidable languages is closed under the operations of: Complementation, Concatenation, and Intersection
I understand that the problem is asking for a proof for the specified Turing machine. My issue derives from not being able to understand what type of structure this problem is proposing, as indicated below:
We say that a class C of languages is…
Totsuka Blade
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-1
votes
1 answer
Algebra for bitwise operators
I am trying to prove that a certain equation, with an operation defined for base 10, is equivalent to another operation (with slightly different numbers) that is only defined in base 2 (&, |, etc.). I am trying to prove this through induction, but…
Altoid_10
- 11