Definitions for overspill
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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
That which spills over.
New towns were to accommodate overspill from established cities.
To spill over, to overflow, to spill out of.
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.
spillover, spill over
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