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Re: [HM] Counting from Zero
Posted:
Jul 26, 2005 9:12 AM
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Dear Sam:
Your query brings to mind the conundrum about naming sets of numbers. In
the preparation of elementary school teachers, we (!) instruct them first
about the natural numbers {1, 2, 3, ...}, then move on to whole numbers {0,
1, 2, 3, ....}, and next the integers { -2, -1, 0, 1, 2, . . .}. Now the
word INTEGER is from the Latin language and means WHOLE. Ergo, the whole
numbers are integers?
Then of course, we have the counting numbers {1, 2, 3, . . .} (pace JHC).
They are also called the NATURAL numbers, because that is the way we count.
Now when we count, there are objects in front of us. (If there are no
objects, then we don't count.) Suppose there are a bell, book, and candle
on a able and we are asked to count them. So, pointing to the bell, we say
"One," to the book "Two", and to the candle "Three". Why is the book TWO?
or the candle THREE?
This example I have used many times with future elementary school teachers
to get across to them the Greek concept of number, a collection of units.
Each of the above three is ONE. When I add the second one to the first one,
I have created a collection and its number is two; etc. This is the
natural way of counting. (Hence, the identity: natural numbers = counting
numbers) For the first time, many of the students understood what it meant
to count.
Years ago I read a statement by by a mathematician (Edward Kastner??), "In
teaching mathematics, it is not necessary to tell the whole truth. But what
you teach must be truthful." Bertrand Russel contributed greatly to the
development of number theory. It is best left to theoreticians and not
exposed to children.
Best wishes!
Barney Hughes
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