Infinity symbol Infinity symbol The infinity symbol (sometimes called the lemniscate) is a mathematical symbol representing the concept of infinity. The shape of a sideways figure eight has a long pedigree; for instance, it appears in the cross of Saint Boniface, wrapped around the bars of a Latin cross. However, John Wallis is credited with introducing the infinity symbol with its mathematical meaning in 1655, in his "De sectionibus conicis". Wallis did not explain his choice of this symbol, but it has been conjectured to be a variant form of a Roman numeral for 1,000 (originally CIƆ, also CƆ), which was sometimes
Determining the number of clusters in a data set of "G" "p"-dimensional Gaussian distributions with common covariance. Then for any fixed "K" less than "G", the distortion of a clustering as "p" goes to infinity is infinite. Intuitively, this means that a clustering of less than the correct number of clusters is unable to describe asymptotically high-dimensional data, causing the distortion to increase without limit. If, as described above, "K" is made an increasing function of "p", namely, formula_5, the same result as above is achieved, with the value of the distortion in the limit as "p" goes to infinity being equal to formula_10. Correspondingly, there is the same