# Non-standard analysis: Quiz

Question 1: More generally, non-standard analysis is any form of mathematics that relies on non-standard models and the ________.
Complex numberTransfer principleReal numberHyperreal number

Question 2: Nelson introduced an entirely axiomatic formulation of non-standard analysis that he called ________ or IST.
ConsistencyInternal set theoryReal numberLogic

Question 3: The superstructure over the real numbers includes a wealth of mathematical structures: For instance, it contains ________ copies of all separable metric spaces and metrizable topological vector spaces.
IsomorphismEquivalence relationBinary relationAutomorphism

Question 4: As noted in the article on hyperreal numbers, these formulations were widely criticized by ________ and others.
George BerkeleyImmanuel KantRené DescartesBertrand Russell

Question 5: Jerome Keisler has written an elementary text on ________ that develops differential and integral calculus using the hyperreal numbers, which include infinitesimal elements.
Non-standard calculusHyperreal numberInfinitesimal calculusNon-standard analysis

Question 6: See the article on ________ for a discussion of some of the relevant ideas.
Surreal numberComplex numberOrdinal numberHyperreal number

Question 7: Moreover it is possible to consider a simpler form of saturation called ________ saturation.
Georg CantorCardinal numberSet (mathematics)Countable set

Question 8: For example, proving the ________ for differentiation is easier in a non-standard setting.

Question 9: Elements of *R are called ________.
Complex numberOrdinal numberSurreal numberHyperreal number

Question 10: Starting from a superstructure V(S) one constructs another object *V(S) using the ultrapower construction together with a mapping V(S) → *V(S) which satisfies the ________.
Real numberHyperreal numberTransfer principleComplex number