It is a lot easier to prove that you don't love someone than it is to prove that you do, but one of the best 'proofs' I know is the desire to devote time to the person with no expectation of any sort of compensation, including gratitude, in return. — Marilyn vos Savant 14 I ...
Proofs God Exists: How did the universe or earth get created if God didn't create it? There was nothing before the universe so how did it come to be as something can't come from nothing. 0 + 0 can't equal 1. The common reply is "well how was God created" but that ans...
For every rate R<C , there exists a sequence of \left(\lceil 2^{NR}\rceil,N\right) codes with average probability of error \overline{P}_e^{\left(N\right)}\left(\mathcal{C}\right) that tends to zero as N\to\infty. The proof of achievability uses random coding and joint typica...
This document defines a technique for generating a succinct non-interactive zero-knowledge argument that for a given input x and a circuit C , there exists a witness w , such that C(x,w) evaluates to 0. The technique here combines the MPC-in-the-he
Since ψ has exactly n vanishing moments, (6.15) proves that |Wg(u,s)|∼Ksn+1/2g(n)(u). We suppose that g(n)(u)≠ 0. For τ(q)≤ (n + 1/2)q, since |Wg(u,s)|q∼sq(n+1/2) has a faster asymptotic decay than sτ(q) when s goes to zero, one can verify that...
Consider a function f that represents the speed of a car. The speed of the car is continuous since there are no points at which it would not exists (note that when the car is not moving its speed is zero). If the speed of a car is considered on a certain time interval, and the ...
Consider that P cannot be the zero polynomial. This does not correspond to the conclusion of the lemma 1, which means that there exists some 1≤i≤n s.t. the degree of P in xi is at least ti+1. Take i=n for notational convenience. Then we know that some nonzero monomial c∏i=...
As a result, the set of jobs that start processing before D provides a solution to even-odd partition problem, which indicates that a feasible schedule for instance I implies a solution to even-odd partition. By combining Lemma 1 and the proof above, there exists a schedule for this ...
In contrast, a constructive proof establishes that a particular object exists by providing a method of finding it. A famous example of a nonconstructive proof shows that there exist two irrational numbers a and b such that a^b is a rational number:...
Beyond a reasonable doubt establishes that no other reasonable explanation exists other than the evidence presented to the court. Commonly used in criminal prosecutions, such as murder trials, this is the highest legal standard of proof. Civil Case vs. Criminal Case ...