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2 days ago · The most common method for proving conjectures is direct proof. This method will be used to prove the lattice problem above. Prove that the number of segments connecting an \(n\times n\) lattice is \(2n(n+1)\).
5 days ago · In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample mean converges to a standard normal distribution. This holds even if the original variables themselves are not normally distributed.
5 days ago · A common proof identifies the unit ball with the weak-* topology as a closed subset of a product of compact sets with the product topology. As a consequence of Tychonoff's theorem, this product, and hence the unit ball within, is compact.
3 days ago · Then a proof is sketched that, if one uses the definition of exponentiation given in preceding sections, one has exp ( x ) = e x . {\displaystyle \exp(x)=e^{x}.} There are many equivalent ways to define the exponential function , one of them being
2 days ago · To prove a conclusion from a set of premises, is a transformation of the propositions using certain inference rules. This abstraction of the formulation of arguments is one of the central themes in formal logic.
1 hour ago · CONCORD, N.H. (AP) — A lawsuit filed Monday challenges a New Hampshire law that would require proof of U.S. citizenship when registering to vote and photo identification when casting a ballot, saying it is one of the most restrictive voting laws in the nation. The new law was set to take effect after the November elections.
5 days ago · The Chinese remainder theorem can be useful for proofs. Show that there exist \(99\) consecutive integers \(a_1, a_2, \ldots, a_{99}\) such that each \(a_i\) is divisible by the cube of some integer greater than 1.
