![]() | This article is rated B-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
|
This page has archives. Sections older than 90 days may be automatically archived by ClueBot III when more than 5 sections are present. |
in the subsection on the "intuitive approach", the following claim is made: "the true infinitesimals are the classes of sequences that contain a sequence converging to zero." This is an oversimplification that will not always be true. Depending on foundational assumptions, certain infinitesimal classes may not be representable by sequences tending to zero. Tkuvho ( talk) 13:01, 23 June 2010 (UTC)
The sentence "The infinitesimals can be represented by the non-vanishing sequences converging to zero in the usual sense, that is with respect to the Fréchet filter" is just plain wrong. Tkuvho ( talk) 13:08, 23 June 2010 (UTC)
The phrase "However, there may be infinitesimals not represented by null sequences; see P-point" was deleted in a recent edit. Why was it deleted? Tkuvho ( talk) 11:51, 7 May 2013 (UTC)
The section headed "Properties of infinitesimals and infinite numbers" does not mention any properties of infinite numbers. Shame, because that's what I wanted to know about. Tesspub ( talk) 10:28, 29 August 2014 (UTC)
This is incorrect; using Keisler's treatment and are infinitesimal increments along the tangent line while and are infinitesimal increments along the curve. So . 58.169.240.244 ( talk) 15:17, 4 May 2015 (UTC)
This sentence "The transfer principle, however, doesn't mean that R and *R have identical behavior" is misleading. R and *R do have identical behavior as long as you don't write down statements that involve both standard and non-standard numbers. In the example, is a non-standard real whereas the dots ... are interpreted in the standard way (with the set of standard integers) (in other words, with a set that is undefinable in *R). Mixing standard with non-standard is really the only way that "non-identical" behavior can occur. If you stick with "all standard" or "all non-standard" then the behavior is identical. MvH ( talk) 21:58, 7 February 2020 (UTC)
![]() | This article is rated B-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
|
This page has archives. Sections older than 90 days may be automatically archived by ClueBot III when more than 5 sections are present. |
in the subsection on the "intuitive approach", the following claim is made: "the true infinitesimals are the classes of sequences that contain a sequence converging to zero." This is an oversimplification that will not always be true. Depending on foundational assumptions, certain infinitesimal classes may not be representable by sequences tending to zero. Tkuvho ( talk) 13:01, 23 June 2010 (UTC)
The sentence "The infinitesimals can be represented by the non-vanishing sequences converging to zero in the usual sense, that is with respect to the Fréchet filter" is just plain wrong. Tkuvho ( talk) 13:08, 23 June 2010 (UTC)
The phrase "However, there may be infinitesimals not represented by null sequences; see P-point" was deleted in a recent edit. Why was it deleted? Tkuvho ( talk) 11:51, 7 May 2013 (UTC)
The section headed "Properties of infinitesimals and infinite numbers" does not mention any properties of infinite numbers. Shame, because that's what I wanted to know about. Tesspub ( talk) 10:28, 29 August 2014 (UTC)
This is incorrect; using Keisler's treatment and are infinitesimal increments along the tangent line while and are infinitesimal increments along the curve. So . 58.169.240.244 ( talk) 15:17, 4 May 2015 (UTC)
This sentence "The transfer principle, however, doesn't mean that R and *R have identical behavior" is misleading. R and *R do have identical behavior as long as you don't write down statements that involve both standard and non-standard numbers. In the example, is a non-standard real whereas the dots ... are interpreted in the standard way (with the set of standard integers) (in other words, with a set that is undefinable in *R). Mixing standard with non-standard is really the only way that "non-identical" behavior can occur. If you stick with "all standard" or "all non-standard" then the behavior is identical. MvH ( talk) 21:58, 7 February 2020 (UTC)