@MISC{Shapiro_bignumbers, author = {Daniel B. Shapiro}, title = {Big Numbers}, year = {} }

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Abstract

What is the largest number you can think of? (Here I am asking about actual counting numbers, not “infinity”.) People answer this question in different ways depending on how many numbers they know. Preschoolers might answer “one hundred ” while others might answer “a zillion ” or “a skillion ” or (my favorite) “an impossibillion”. But these terms are not really the standard names for any numbers. When I first learned about large numbers (a large number of years ago), I read about a “googol”. This nonsense name was made up around 1940 by authors Kasner and Newman to represent the number 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000. This is a one followed by one hundred zeros. It is a big number. There are fewer than a googol atoms in the entire visible universe (even if all that space was packed solid with atoms). A googolplex was then defined to equal a one followed by a googol zeros. Writing out a googolplex in the usual base ten notation would take up a lot of paper! Here is a more compact way to write such large numbers. If b and n are whole numbers then b n (read “b to the n”) is the product of n copies of b. For example,