# Opinion 14: It Is Time to Kick Zero Out of the Elementary
School Curriculum

## By: Doron Zeilberger

Written: March 19, 1997

Once upon a time there was a genius who invented Zero.
So when one had to multiply XIX by CIX all one had
to do is write it as 19x109, and perform long multiplication.
Hence one hundred and nine was coded into a vector of digits of length
[log(109)]+1 (decimal logarithms.)

This algorithm is fairly efficient, but is nowadays obsolete,
since we have Fast Fourier Transform, and besides,
we can use a calculator. Nevertheless, we torture our poor
fourth- and fifth-graders, by programming them into
performing these boring and uninspiring
tasks. Of course, neither students nor teacher have
any clue why the method works.

If we want to teach our kids
the ideas behind multiplication, we would be much better off
going back to the sparse, rather than dense, notation.
In particular, get rid of this unintuitive and overly abstract
concept of zero. If there is nothing to write, don't write it!

So let T:=ten, and write XIX as T+9 and CIX as TxT+9, then
to multiply them, let them do: (T+9)(TT+9)=
TTT+9T+9TT+(8T+1)=TTT+9TT+(9+8)T+1=TTT+9TT+(T+7)T+1=
TTT+9TT+TT+7T+1=TTT+(9+1)TT+7T+1=TTT+TTT+7T+1=2TTT+7T+1.

This way, they would be able to understand much better the ideas behind the
positional system. In fact, they should only do it in base
2, but again, without using zero.

Read Dick Askey's response.
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