30 abr. 2014

Counting numbers

I was a child when I had the question: till what number we can count?
Today I know that there is an infinite set of numbers but my question still remains with a little change: how many of the numbers have a name?

You know that you can count units from 1 to 9 (one to nine). After, you can group the units in tenths from 10 to 90 (ten to ninety), and then you can group the numbers in hundreds from 100 to 900 (one hundred to nine hundred). After that, numbers can be grouped in thousands from 1000 to 9000 (one thousand to nine thousands), tenths of thousands from 10000 to 90000 (ten thousands to ninety thousands), millions from 1000 000 to 9 000 000 (one million to nine millions), tenths of millions from 10 000 000 to 90 000 000 (ten millions to ninety millions), hundreds of millions 100 000 000 to 900 000 000 (one hundred millions to nine hundred millions) and billions 1000 000 000 to 900 000 000 (one billion to nine billions). In between of all these numbers you can find a name for everyone.
If you take any number between 1 and 99 999 999, for example 118 967 524 you can write down a name for it, but how about higher numbers?
From billions and so on, we start to have many problems for their names.
In English spoken countries, they use the short scale for numeration that uses the name billions for numbers between 1000 000 000 to 9000 000 000. However most European and Latin American countries uses the long scale for numeration and numbers between 1000 000 000 to 9000 000 000 are named one thousand million and nine thousand millions.

When I was a kid, I used to put the name to the number 1 followed by one or more zeros until I knew the name. One day an aunt came to see my pages and said that there was no sense to count so many numbers because there are no real things to be counted by them. Maybe she was right in our real and close world. In real life we scarcely see big numbers, well if you do not take into account internet of course! But maybe the difference between short and long scales makes sense if you talk about money. In Forbes, you find people named billionaires but in countries that use long scale numeration they are multimillionaires instead.
But how about higher and higher numbers?
If you use scientific notation it is easy to write the numbers with fewer symbols. Instead of writing 10, you write 101, and 102 if you want to write 100. The little superscript is the exponent that indicates how many zeros the 1 has after him (to the right).
The word million appears in English books from the XIII century and billions and trillions have the origin in France of the XV century. In 1484, the words quadrillion, quyllion, sixlion, septyllion, ottyllion and nonyllion appeared in a French book and have been translated to the English (not necessarily with the same meaning).
When you start to count it is logic to ask till what number you can count. Some people do not go more than millions or billions, some other stopped before.
But how about who went further?
In 1938 a nephew of the American mathematician Edwar Kasner named googol to the number 1 followed by 100 zeros and googolplex to the number 1 followed by the zeros that you can write before people feel tired. But the problem is that everyone is tired not at the same time. For that reason, Kasner named googolplex at the number 1 followed by a googol of zeros! That so huge number is impossible to write in our universe! (By the way, the search engine Google is based in the name googol).

And there are many more numbers bigger than that…

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