Re: ONE
- From: "John Thingstad" <john.thingstad@xxxxxxxxx>
- Date: Thu, 22 Dec 2005 12:09:39 +0100
On Thu, 22 Dec 2005 11:30:11 +0100, alan <monguin61@xxxxxxxxx> wrote:
"One" as a word representing a numeral is defined as the multiplicative identity element in the integer/rational/real/complex/etc number system. I can't call myself an expert, but in the term "one-to-one relation" I don't believe the "one" here refers to the same concept. Which one are you asking about?
one to one relations take one region in one mapping to exactly one region in
another mapping. So 1 refers to one region.
Say in DB theory a one-to-one relation means one object relates to only one
other object as opposed to many. Say one car to one driver. Here region is defined as
one objekt and many attributes.
For example: car(car-id, diver-id, passenger-list-id ...) driver(driver-id, person-id) So a one to one relation here between car and driver means SELECT * FROM car, driver WHERE car.diver-id = driver.driver-id
In function analysis one-to-one region is traditionally assosiated with point.
In traditional analysis one talked about infetesimals.
So one point made sense as a definition for region.
Modern analysis takes a slightly different approach basically a abratary small delta. So region here would be a delta region about a point but still unique to the point.
I suppose this is the source of the confusion.
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