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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How to prove (x+y)/z + (y+z)/x + (x+z)/y>=6 when x,y,z>0
This question actually had two parts. In the first part I had to prove that a + 1/a >=2. I proved it by rearranging it to (a-1)^2 >= 0, which is always true.
So, I thought the second problem would require a similar method.
(x+y)/z + (y+z)/x +…
Pup
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Differentiating between learning and memorisation in Artificial Neural Networks
Is there a good resource that clearly explains the difference between learning and memorisation of artificical neural networks - much better if the source contains mathematical explanations and/or proofs.
I have looked online and through literature…
guthik
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Need to prove language L = {a^nb^m: n < m < 2m} is not regular
I don't understand the pumping lemma very well, and could use a simple break down of how to prove something like this.
stacklee
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How do I get complexity with division?
I'm trying to prove/disprove that (n^2 log n + 10) / (n - 10) = O(n log n)
I think it's wrong, since we can separate (n^2 log n)/(n-10) - 10/(n-10), and we can't simplify any further. There is no way to remove the 10s, which would make it n^2 log n…
Andrew Raleigh
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What programming language has the specific purpose of testing concurrent algorithms?
A colleague of mine has written a program that proves that some conditions will not be met after testing an algorithm running multiple concurrent threads trying to find a sequence that might trigger the unwanted condition. He used a computer…
Jader Dias
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Proof by contradiction
I'm trying to do a proof by contradiction, but don't quite understand how to write it down formally or how to come to an answer in this case. I'm doing a conditional statement.
The problem I'm trying to solve is "Given the premises, h ^ ~r and (h^n)…
Howard P
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euclid's lemma for prime numbers
Euclid's lemma says that if p divides ab, then p divides a or p divides b.
If this is the case then p is prime.
What about when p=4, a=8 and b=9.
p| ab => p|72
then,
(p|8 or p|9) is true.
This infers that p is prime.
But 4 is not a prime number.
I…
tidbits
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Mathematical proof that there is no infitely recursive selector in CSS?
Some have claimed that there exists no CSS selector that can crash a browser by entering an infinite loop as it tries to find all matching elements in the document ree. Can this be proved mathematically? If so, how?
Peter Thiel
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How does my professor come up with the recursive case in this algorithm analysis?
My professor gave us the following explanation for the recursive algorithm for finding the permutations of a set of numbers:
When he has (T(m+1), n-1)) where does that come from? Why is it m+1 and n-1? I'm really confused as to where that comes…
Doug Smith
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Two strings are anagrams of each other if and only if the sum and product of the characters of the strings are same. How?
I was reading an algorithmic problem at
http://learn.hackerearth.com/question/314/finding-non-anagramic-strings-in-a-list/
I came across the following claim:
Two strings (of same size) are anagrams of each other if and only if the sum and product…
Steve M
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Mathematical induction proofs
For my theory of computation class, we are supposed to do some review/practice problems to work off the rust and make sure we are ready for the course. Some of the problems are induction proofs. I did this at one time, but apparently it has…
Bryan
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longest common subsequence with linear memory usage
I'm trying to find an algorithm which uses linear space of memory for:
Given two strings x and y over an arbitrary alphabet, determine their longest common sub sequence.
Mike
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Prove max(O(f(n)), O(g(n)))=O(max(f(n), g(n))
Prove max(O(f(n)), O(g(n)))=O(max(f(n), g(n))
It does make sense, but so far I don't have any idea how to actually prove it.
Any input would be appreciated.
EatEmAll
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Why can't all existential binders be replaced by unique constants during skolemization?
When using skolemization to replace existentially quantified variables in an expression, any existential bound at the top level can be replaced by a new globally unique constant, however if the existential is under a universal quantification it…
Jean-Baptiste
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Order of complexity proofs. Show that if f1 is O(f2) and f2 is O(g), then f1 is O(g)
Show that if f1 is O(f2) and f2 is O(g), then f1 is O(g).
I did the following: Using the definition of big-Oh, we need to show that there exist n_0 and C such that f1 ≤ Cf2 is valid for some constant C > 0 and for all n >= n0. Similarly, f2 ≤ C1g.…
Buddy
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