Googolplex

From Academic Kids

A googolplex is the number <math>10^{10^{100}}<math> (or <math>{10}^\mbox{10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000}<math>, or <math>{10}^\mbox{googol}<math>), that is, 1 followed by a googol zeroes. The term googol was coined by the nephew of mathematician Edward Kasner. Googolplex was coined by Kasner to define an especially large number by extension from his nephew's idea. [1] (http://www.google.com/corporate/index.html)

A googol is greater than the number of particles in the known universe, which has been variously estimated from 1072 up to 1087. Since this is less than the number of zeroes in a googolplex, it would not be possible to write down or store a googolplex in decimal notation, even if all the matter in the known universe were converted into paper and ink or disk drives.

Thinking of this another way, consider printing the digits of a googolplex in unreadable, 1-point font. TeX 1pt font is .3514598mm per digit, which means it would take about <math>3.5*10^{96} <math> meters to write in one point font. The known universe is estimated at <math> 7.4*10^{26} <math> meters in diameter, which means the distance to write the digits would be about <math>4.7*10^{69} <math> times the diameter of the known universe.

Even then, the magnitude of the googolplex is not as large as some of the specially defined extraordinarily large numbers, such as those using Knuth's up-arrow notation or Steinhaus-Moser notation. Even more simply, one can name numbers larger than a googleplex with fewer symbols, for example,

<math>9^{9^{9^{9^{9^9}}}},

<math> which is much much larger.

See also

External links

fr:Gogolplex hu:Googolplex no:Googolplex ru:Гуголплекс fi:Googolplex sv:Googolplex

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