# Definitions for **overspill**

### This page provides all possible meanings and translations of the word **overspill**

### Princeton's WordNet

overspill(noun)

the relocation of people from overcrowded cities; they are accommodated in new houses or apartments in smaller towns

overflow, runoff, overspill(noun)

the occurrence of surplus liquid (as water) exceeding the limit or capacity

### Wiktionary

overspill(Noun)

That which spills over.

New towns were to accommodate overspill from established cities.

overspill(Verb)

To spill over, to overflow, to spill out of.

### Freebase

Overspill

In non-standard analysis, a branch of mathematics, overspill 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 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 hyperreal. ⁕If an internal set contains N it contains an unbounded element of *N.

# Translation

#### Find a translation for the **overspill** definition in other languages:

Select another language:

#### Discuss these overspill definitions with the community:

# Citation

## Use the citation below to add this definition to your bibliography:

"overspill." *Definitions.net.* STANDS4 LLC, 2014. Web. 1 Nov. 2014. <http://www.definitions.net/definition/overspill>.