Posted on 01/24/2009 6:43:23 PM PST by Daffynition
For seventy years, a prayer book moldered in the closet of a family in France, passed down from one generation to the next. Its mildewed parchment pages were stiff and contorted, tarnished by burn marks and waxy smudges. Behind the text of the prayers, faint Greek letters marched in lines up the page, with an occasional diagram disappearing into the spine.
The owners wondered if the strange book might have some value, so they took it to Christie's Auction House of London. And in 1998, Christie's auctioned it off—for two million dollars.
For this was not just a prayer book. The faint Greek inscriptions and accompanying diagrams were, in fact, the only surviving copies of several works by the great Greek mathematician Archimedes.
An intensive research effort over the last nine years has led to the decoding of much of the almost-obliterated Greek text. The results were more revolutionary than anyone had expected. The researchers have discovered that Archimedes was working out principles that, centuries later, would form the heart of calculus and that he had a more sophisticated understanding of the concept of infinity than anyone had realized. [snip]
(Excerpt) Read more at sciencenews.org ...
But that is the point of the thread - calculus is multiplying by zero, isn’t it?
The argument about math concepts being invented or discovered is a great one and not yet settled!
The thing you posted in #9
I'd even go as far as calling it groovy.
Ahhh...I figured I was missing something obvious. I was looking for the "divide by zero" part and couldn't find it. There it is!
Well since a=b=1 ...and then a-b=0
your cancellation is equivalent to dividing by zero...
which is usually considered to not be a permitted operation ...leads to strange results...
;)
I guess it depends on whether math is real or observed.
But you accept multiplying by zero, and coming up with a non-zero answer? An integral?
Are you always this selective in which laws you obey?
You sound like a liberal. You know, selective enforcement, rule by exception,...
;)
A small number is NOT zero...if that is what you mean by multiplying by zero.....
Yes, it is. An integral is just the sum of the areas of a bunch of boxes, who have height = whatevever, and width = zero.
Anyway, the sum of the area of the zero-width boxes is the area under the curve.
That, my friend, is calculus.
It is define as the limit as dx ->0.
The limit of dx->0 is, by definition, ZERO.
“The argument about math concepts being invented or discovered is a great one and not yet settled!”
OBTW, can you tell me wether the countable chain condition implies that a space is compact? I have been puzzling over that for about 20 years.
This is not true at all. The numeral 0 originated as a place holder in positional number notation, and while this ultimately suggests that it ought to be treated as a number itself, its status as a place holder by no means requires it.
In fact, it's easy to see that zero as a number still has a shaky status in popular thinking. For example, the "Cash Back" screen on a card reader at a pay station in a store will have, e.g. $40, $20, $10, NO ... the last meaning, "NO, I don't want cash back", so there isn't any NUMBER of dollars I'm getting back.
I saw the same thing in my childrens' grade school class room, years ago. The class had a small chart showing the number of children in the class having birthdays in each month. Months with no birthdays were left blank ( or perhaps marked N/A ?? ) ... There was no NUMBER of birthdays for that month.
Wait, they had months where no kids were born?
Well, that would be unusual.
God, I rue the day I god that degree in abstract math. Now that is going to keep me up nights...
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