Guo Musical Instrument Company Guo Musical Instrument Company Guo Musical Instrument Company (GMIC) is a Taiwan-based musical instrument manufacturer, specializing in flutes, piccolos, flute head joints, and saxophone necks and head joints. Founded by Geoffrey Guo in 1988, GMIC offers its products for sale online and through various retailers all over the world. Some of its instruments include a tenor flute, a G soprano flute, grenaditte flutes and a new C flute design called a Tocco flute. Many of these models of flutes and piccolos come in many different colors. In 2004, Geoffrey Guo and flute professor Mark Dannenbring developed the grenaditte flute. This
Proof that e is irrational numbers. Still another proof can be obtained from the fact that Define formula_11 as follows: Then: which implies: for any integer formula_15 Note that formula_16 is always an integer. Assume formula_17 is rational, so, formula_18 where formula_19 are co-prime and formula_20 It's possible to appropriately choose formula_21 so that formula_22 is an integer i.e. formula_23 Hence, for this choice, the difference between formula_22 and formula_16 would be an integer. But from the above inequality, that's impossible.So, formula_17 is irrational. This means that formula_27 is irrational. In 1840, Liouville published a proof of the fact that "e" is irrational followed by