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Copyright 2002, all rights reserved
WONDER QUEST with April Holladay, A Weekly Column * January 9, 2002* Albuquerque
Zero, a number!
![[Teaching Ideas for Primary Teachers] Each row-- top: Hindu, middle: Arabic/European, 1442 AD](zero.jpg) Q: Is zero a number? -Peter E., Albuquerque, New Mexico
A: Yes, zero is a number but you are not alone if you wonder why. Indian mathematicians first came up
with the number idea around 650 AD. Originally, perhaps as early as 200 AD, they used zero as a
placeholder in another number. For example, in our notation: 216 is a different number than 2016. This
use of zero advanced trade, commerce, and bookkeeping but does not qualify zero as a number. Zero, in
its place-keeping function, is a kind of punctuation mark to help us interpret numbers correctly.
[Teaching Ideas for Primary Teachers] Each row-- top: Hindu, middle: Arabic/European, 1442 AD
In about 630 AD, the great Indian mathematician, Brahmagupta, wrote the rules for arithmetic involving
zero and negative numbers. This masterpiece brings zero into the realm of numbers. Zero is a count of
nothing.
By the way, although Brahmagupta devised good rules for addition and subtraction, his rule for division by zero fails (e.g., 0/0 = 0). Not
until 1828, did a German, Martin Ohm, successfully handle this problem: simply by outlawing division by zero. It is forbidden; else one
obtains untrue results using other rules of arithmetic.
Zero advances human insight into numbers. Numbers, basically, is the notion of counting. Three pebbles stand for three sheep. The
number three is an abstraction from all collections containing three actual things.
Zero is a step farther into the abstract. Until then, each number stood for a count of something concrete. Zero, however, is a count of
the elements in the completely empty set: nothing.
"...the word 'number' (in various languages and at various times) has had different meanings," says Andrew Gleason, mathematics
professor emeritus at Harvard.
In classic Greek times it meant an integer at least three. Now it includes negative numbers (-1, -2...) and more.
People argue whether -1 or -2 is a number because you can't have -2 sheep. "This argument ... is pointless," says Gleason, "because it's
a matter of definition... On the other hand, it seems that there is a super-convention that restricts the word 'number' to entities which
have some sort of arithmetic. Thus, if you have two numbers ... you would expect that it would be meaningful to add them."
Telephone numbers, aren't really numbers, he says, because adding them has no meaning. Zero is a number, by definition and the rules
of arithmetic. Add zero to any number and you obtain that number.
Further Surfing:
U of St Andrews, Scotland: A history of zero
Teaching Ideas: Nine number systems used through history
Comment
Readers' Comments:
- It seems to me that the number zero has created as many problems as it has
solved. Functions such as 1/R^2 can neither be calculated nor measured at the
origin. Science depends upon measurable numbers not upon undefined divisions.
Does some form of mathematics exist that does not lead to undefined divisions?
Bill Seattle WA USA
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