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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Where is the proof for complement of base 10 integer formula?
So,for https://leetcode.com/problems/complement-of-base-10-integer/discuss/879910/Java-100-faster-solution-trick-to-find-2(digits-of-N)-1-greater-(11111)-and-subtract-N-from-it can anyone provide the proof to why 2^(length of binary digits) - 1…
guest223421
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1 answer
Finding these three algorithm's run time
Hi I am having a tough time showing the run time of these three algorithms for T(n). Assumptions include T(0)=0.
1) This one i know is close to Fibonacci so i know it's close to O(n) time but having trouble showing that:
T(n) = T(n-1) + T(n-2) +1
2)…
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votes
2 answers
How to set up an inductive proof in haskell?
I need to prove
f (g xs) == g (f xs)
whenver xs is a finite list of Ints.
Assume both f and g are of type [Int]->[Int]
user3358850
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2 answers
Proof n^2 - 4n = Big-Theta(2^n)
I should prove or disprove the equation
n^2 - 4n = Big-Theta(2^n)
As far as i know i need to prove the following two equations:
f = O(g)
g = O(f)
I started to solve f = O(g)
n^2 - 4n = c * 2^n // use log
2log(n) - log(4n) = log(c) * n *…
w1cked
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Simplifying Boolean Expressions
I have constructed truth tables to prove that:
ABC + ABC'+ AB'C A'BC = AB+AC+BC,
but how do i prove it by simplifying the expression? I'm fairly new to boolean algebra and have tried to use the basic identities to figure it out, but can't seem to…
mish1234
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Integral of a sign function proof
Can anyone please prove this expression below? I saw this in a paper and trying to see where it is coming from.
integral(sign(A*w*cos(w*t+phi))*cos(w*t), t, 0, 2*pi/w) = 4/pi*cos(phi)
Baha
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votes
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Proof from Axioms
Given the axioms
Henry owns a bike
Every bike owner loves racing
No one who loves racing buys a scooter.
Either Henry or Bob bought a scooter, which is named Bill
Did Bob buy the scooter?
This is a homework question; it seems almost too easy, so…
Arty
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votes
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Combining a set of fractions
Consider the set {1, 1/2, 1/3, 1/4, 1/5, ..., 1/n}
Choose any two numbers x and y and replace them with x + y + xy
For example, if we choose the numbers 1 and 1/2 , we will replace them by 1 + 1/2 + 1/2 = 2.
If we keep repeating this process until…
a.sankar
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Proof of (w * w^R)^R = w*w^R
Question: if w exist in T*, prove that (w * w^R)^R = w * w^R
Hi, I am new to theories of algorithms, and I am having trouble understanding how to prove this, if someone can hint me towards the right direction that would be much appreciated.
Note: R…
Nightmare
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votes
3 answers
Formal proof for what algorithm return
I need to formal proof that below algorithm return 1 for n = 1 and 0 in other cases.
function K( n: word): word;
begin
if (n < 2) then K := n
else K := K(n − 1) * K(n − 2);
end;
Anyone could help? Thank you
Jo Dung
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votes
2 answers
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1 answer
How can I proof a difficult big o notation?
I can easily understand how to proof a simple big o notation like n5 + 3n3 ∈ O(n5).
But how can I proof something more complex like 3n or 2n ∉ O(nk)?
Dieter Brow
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Direct proof sequence of n length
We denote a(n) as the number of sequence of n values of 0,1 and 2 where the value 0 can't be next to another 0 in the sequence.
For example, we can have (0,1,0,2), but not (0,0,2,1)
Prove by direct proof that a(n) = 2a(n-1) + 2a(n-2) for n ≥ 3
user2420374
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votes
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Prove for 928675*2^n=0(2^n) Big-0notation complexity
I am supposed to Prove that 92675*2^n=0(2^n) and use the mathematical definition of 0(f(n)). I came up with following answer not sure if this is the right way to approach it though
Answer: Since 92875 is a constant, we can replace it with K and…
saleh mohsen
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votes
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Big Oh and Omega notation complexity proof
Prove that n3 is not in O(n2)
Prove that n3 is not in OMEGA(n4)
user3358850
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