Posted on 01/24/2009 6:43:23 PM PST by Daffynition
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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