false and false is false logically. The result of an expression using the && operator is determined based on these rules: If the left side of the expression is “falsey”, the expression will return the left side. Do two false make a true? No. Formal logic (valid reasoning) guarantees onlyRead More →
Since the correlation is a continuous function of c, the intermediate value theorem implies there is some particular value of c that makes the correlation 0. That value is approximately 1.54. In that case, X and Y are uncorrelated, but they are clearly not independent, since X completely determines Y.Read More →
Definition(Completeness) A metric vector space X with metric d is complete if any Cauchy sequence {xn}, there is x0 ∈ X such that d(xn,x0) < ϵ for any ϵ > 0 and n large enough. Remark A complete normed vector space is named a Banach Space and a complete innerRead More →
For a function to be continuous at a point, it must be defined at that point, its limit must exist at the point, and the value of the function at that point must equal the value of the limit at that point. Discontinuities may be classified as removable, jump, orRead More →