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### How Far Can You Count?

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Date: Fri, 6 Jan 1995 14:09:20 +22305931 (CST)
From: Leslie Rennie

Dear Dr. Math,

My name is Danielle Hummer. I am a student at Converse School in
Beloit. Miss L. Rennie is connected to the Internet and we have this
question: "How far can you count after millions, billions, and trillions.
In other words, what is the highest point you can count to?"

I will look forward to hearing from you. Thanks for your help!

Miss Rennie
Danielle Hummer
renniel@beloit.edu

P.S. Beloit is in Wisconsin!
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Date: 6 Jan 1995 23:42:37 -0500
From: Dr. Ken

Hello there!

Your question is an interesting one.  As you may know, there is no highest
number.  If there were some number that was the biggest number, we could
just add one to it, and we'd get something bigger.  So that couldn't have
been the highest number at all.

But you're asking what the highest number that you can _count_ up to is.
What I think this means is "what is the highest number that has a name,
and such that all the positive numbers less than it have a name?"

To be honest, the answer depends on who you ask.  Even the number
"billion" can mean either a 1 with 9 zeroes, or a 1 with 12 zeroes.  And
that's all within the English language (the first is the American system,
and the second is the British system).  I was pretty shocked to find that
out.

Anyway, theoretically, you can count up as high as you want to.  The
names for the numbers are taken from the Greek words for numbers:
If you look in most dictionaries under the word "number", you'll get a much
better listing of high numbers than I can give you.  They usually go up
pretty high.

In theory, you're not going to run out of names.  But eventually, of course,
you will.  I mean, there are only so many names, and there are infinitely
many numbers (I'm afraid that I don't know how high numbers have been
named in the normal way).  That's one reason that mathematicians don't
often write out the word "billion" or the words "six billion fourteen
million two hundred eighty thousand seven hundred and four"; instead, they
usually write 1,000,000,000 and 6,014,280,704.

I hope that I've said something useful to you.  I guess most of what I said
is "uh, I don't know.  I try not to think about stuff like that.  Those
numbers are too big."

Note that if you even tried to count to a billion, and you counted all day
and all night, counting one number per second, it would take you over 30
years to do it.

-Ken "Dr." Math
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