Another interesting property of the Arabic system is the fact that there is no limit to how
large a numeral you can represent. Even if a string of digits is hundreds of miles long, even
if it circles the earth, even if it goes from the earth to the moon—all you have to do is put a
nonzero digit on the left or any digit on the right, and you get the representation for a larger
whole number. Mathematicians use the term finite to describe anything that ends somewhere.
No matter how large a whole number you want to express, the Arabic system lets you do it in
a finite number of digits, and every single one of those digits is from the basic set of 0 through 9.
You don’t have to keep inventing new symbols when numbers get arbitrarily large, as people
did when the Roman system ruled.
Every imaginable number can be represented as an Arabic numeral that contains a finite
number of digits. But there is no limit to the number of whole numbers you can denote that
way. The group, or set, of all whole numbers is said to be infinite (not finite). That means there
is no largest whole number.What about “infinity”?
That elusive thing we call “infinity” is entirely different from any whole number, or any other
sort of number people usually imagine. Mathematicians have found more than one type of
“infinity”! Depending on the context, “infinity” can be represented by a lemniscate (∞), the
small Greek letter omega (ω), or the capital Hebrew letter aleph (א) with a numeric subscript
that defines its “density.”Are you confused?
Do you still wonder why the digit 0 is needed? After all, it represents “nothing.” Why bother with commas
or spaces, either?
The quick answer to these questions is that the digit 0 and the comma (or space) are not actually
needed in order to write numerals. The original inventors of the Arabic system put down a dot or a
tiny circle instead of the full-size digit 0. But the cipher and the comma (or space) make errors a lot
less likely.Here’s a challenge!
Imagine a whole number represented by a certain string of digits in the Arabic system. How can you
change the Arabic numeral to make the number a hundred times as large, no matter what the digits hap-
pen to be?Solution
You can make any counting numeral stand for a number a hundred times as large by attaching two ciphers
to its right-hand end. Try it with a few numerals and see. Don’t forget to include the commas where they
belong! For example:- 700 represents a quantity that’s a hundred times as large as 7.
- 1,400 represents a quantity that’s a hundred times as large as 14.
- 78,900 represents a quantity that’s a hundred times as large as 789.
- 1,400,000 represents a quantity that’s a hundred times as large as 14,000.
10 Counting Methods