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What (who) is overspill - definition

PROOF TECHNIQUE IN NON-STANDARD ANALYSIS, IS LESS COMMONLY CALLED OVERFLOW

Internal induction

overspill

¦ noun

1. an instance of spilling over.

2. Brit. a surplus population moving from an overcrowded area to live elsewhere.

overspill

1.

Overspill is used to refer to people who live near a city because there is no room in the city itself. (BRIT)

...new towns built to absorb overspill from nearby cities.

N-UNCOUNT: also a N, oft N n

2.

You can use overspill to refer to things or people which there is no room for in the usual place because it is full.

With the best seats taken, it was ruled that the overspill could stand at the back of the court.

N-UNCOUNT: also a N

Overspill

In nonstandard analysis, a branch of mathematics, overspill (referred to as overflow by Goldblatt (1998, p. 129)) is a widely used proof technique.

https://en.wikipedia.org/wiki/Overspill

Wikipedia

Overspill

In nonstandard analysis, a branch of mathematics, overspill (referred to as overflow by Goldblatt (1998, p. 129)) is a widely used proof technique. It is based on the fact that the set of standard natural numbers N is not an internal subset of the internal set *N of hypernatural numbers.

By applying the induction principle for the standard integers N and the transfer principle we get the principle of internal induction:

For any internal subset A of *N, if

1 is an element of A, and
for every element n of A, n + 1 also belongs to A,

then

A = *N

If N were an internal set, then instantiating the internal induction principle with N, it would follow N = *N which is known not to be the case.

The overspill principle has a number of useful consequences:

The set of standard hyperreals is not internal.
The set of bounded hyperreals is not internal.
The set of infinitesimal hyperreals is not internal.

In particular:

If an internal set contains all infinitesimal non-negative hyperreals, it contains a positive non-infinitesimal (or appreciable) hyperreal.
If an internal set contains N it contains an unlimited (infinite) element of *N.

https://en.wikipedia.org/wiki/Overspill

Examples of use of overspill

1. Hundreds of passengers queued in overspill marquees outside Terminal 4.

2. The overspill galleries in the Commons were pressed into action.

3. The triple attack has been widely seen as an overspill from the Iraq conflict.

4. Otherwise, by necessity, the people mopping up the overspill would spend their entire lives being unfulfilled.

5. But next week even this overspill is likely to be exhausted.