How much is a zillion
Zillion is an indefinite number word for a very large number. Conway and Guy understand the -th zillion generally the -th number on -illion (So in the long ladder the -th power of millions).
Jeffrey Hankins defined a zillion, based on the definition of Googolplex, as a one with a zillion zeros, i.e. as a solution to the equation x = 10x. Solutions to this equation (which actually exist for complex numbers) can be expressed with the analytical continuation of Lambert's W-function leading to a number x delivers its product logarithm, i.e. the number y With x = yey: −Wn(−ln 10) / ln 10. The main value (n = 0) is −0.1191930 ... - 0.7505832 ... also of one n-Azillion are spoken so that words like Bazillion makes sense.
Given that zillions made the Form 106n (long ladder) or 103n + 3 (short ladder), it makes more sense to give the definition x = 106x or. x = 103x + 3 to use. The main value is −W (−6ln 10) / (6ln 10) = −0.1172249… - 0.1595608… i or −W (−3 000ln 10) / (3ln 10) = −0.9904834… - 0 , 3993152 ... i. A zillion could in turn mean a thousand zillion or a one with six zillion three zeros, i.e. a number x, for the x = 106x + 3 applies. Solutions to this equation can be expressed using the analytical continuation of the Lambertian W-function: −Wn(−6 000ln 10) / (6ln 10). The main value (n = 0) is −0.5398940… - 0.2015360… i.
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