<P> In pure mathematics, there are several notational methods for representing large numbers by which the magnitude of a googolplex could be represented, such as tetration, hyperoperation, Knuth's up - arrow notation, Steinhaus--Moser notation, or Conway chained arrow notation . </P> <P> In the PBS science program Cosmos: A Personal Voyage, Episode 9: "The Lives of the Stars", astronomer and television personality Carl Sagan estimated that writing a googolplex in full decimal form (i.e., "10,000,000,000 ...") would be physically impossible, since doing so would require more space than is available in the known universe . </P> <P> One googol is presumed to be greater than the number of atoms in the observable universe, which has been estimated to be approximately 10 . Thus, in the physical world, it is difficult to give examples of numbers that compare to the vastly greater googolplex . However, in analyzing quantum states and black holes, physicist Don Page writes that "determining experimentally whether or not information is lost down black holes of solar mass...would require more than 10 measurements to give a rough determination of the final density matrix after a black hole evaporates". The end of the Universe via Big Freeze without proton decay is expected to be around 10 years into the future . </P> <P> In a separate article, Page shows that the number of states in a black hole with a mass roughly equivalent to the Andromeda Galaxy is in the range of a googolplex . </P>

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