Infinity on High finished the year at number twenty-one on IFPI's list of the "Top 50 Global Best Selling Albums of 2007". "Infinity on High" has shipped over two million copies worldwide. The album also charted inside the top five worldwide, making it the band's most successful and breakthrough album internationally. "Infinity on High" charted all over Europe, debuting at number eight on "Billboard"'s European Albums chart. In Australia, it debuted at its peak of number four on the Australian ARIA Albums Chart. It remained on the Australian chart for a total of fifty weeks, spending its first seven weeks in the top
Vanish at infinity Vanish at infinity In mathematics, a function on a normed vector space is said to vanish at infinity if For example, the function defined on the real line vanishes at infinity. More generally, a function formula_4 on a locally compact space (which may not have a norm) vanishes at infinity if, given any positive number formula_5, there is a compact subset formula_6 such that whenever the point formula_8 lies outside of formula_6. In other words, for each positive number formula_5 the set formula_11 is compact. For a given locally compact space formula_12, the set of such functions (where formula_14 is