Transcendental law of homogeneity (original) (raw)
In mathematics, the transcendental law of homogeneity (TLH) is a heuristic principle enunciated by Gottfried Wilhelm Leibniz most clearly in a 1710 text entitled Symbolismus memorabilis calculi algebraici et infinitesimalis in comparatione potentiarum et differentiarum, et de lege homogeneorum transcendentali. Henk J. M. Bos describes it as the principle to the effect that in a sum involving infinitesimals of different orders, only the lowest-order term must be retained, and the remainder discarded. Thus, if is finite and is infinitesimal, then one sets Similarly,
| Property | Value |
|---|---|
| dbo:abstract | In mathematics, the transcendental law of homogeneity (TLH) is a heuristic principle enunciated by Gottfried Wilhelm Leibniz most clearly in a 1710 text entitled Symbolismus memorabilis calculi algebraici et infinitesimalis in comparatione potentiarum et differentiarum, et de lege homogeneorum transcendentali. Henk J. M. Bos describes it as the principle to the effect that in a sum involving infinitesimals of different orders, only the lowest-order term must be retained, and the remainder discarded. Thus, if is finite and is infinitesimal, then one sets Similarly, where the higher-order term du dv is discarded in accordance with the TLH. A recent study argues that Leibniz's TLH was a precursor of the standard part function over the hyperreals. (en) |
| dbo:wikiPageID | 35889821 (xsd:integer) |
| dbo:wikiPageLength | 2082 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID | 1076046347 (xsd:integer) |
| dbo:wikiPageWikiLink | dbr:Gottfried_Wilhelm_Leibniz dbr:Henk_J._M._Bos dbr:Adequality dbc:History_of_calculus dbr:Law_of_continuity dbc:Gottfried_Wilhelm_Leibniz dbr:Hyperreal_number dbr:Infinitesimal dbr:Standard_part_function |
| dbp:wikiPageUsesTemplate | dbt:Reflist dbt:Short_description dbt:Infinitesimals dbt:Gottfried_Wilhelm_Leibniz |
| dcterms:subject | dbc:History_of_calculus dbc:Gottfried_Wilhelm_Leibniz |
| rdfs:comment | In mathematics, the transcendental law of homogeneity (TLH) is a heuristic principle enunciated by Gottfried Wilhelm Leibniz most clearly in a 1710 text entitled Symbolismus memorabilis calculi algebraici et infinitesimalis in comparatione potentiarum et differentiarum, et de lege homogeneorum transcendentali. Henk J. M. Bos describes it as the principle to the effect that in a sum involving infinitesimals of different orders, only the lowest-order term must be retained, and the remainder discarded. Thus, if is finite and is infinitesimal, then one sets Similarly, (en) |
| rdfs:label | Transcendental law of homogeneity (en) |
| owl:sameAs | freebase:Transcendental law of homogeneity wikidata:Transcendental law of homogeneity https://global.dbpedia.org/id/4wuac |
| prov:wasDerivedFrom | wikipedia-en:Transcendental_law_of_homogeneity?oldid=1076046347&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:Transcendental_law_of_homogeneity |
| is dbo:notableIdea of | dbr:Gottfried_Wilhelm_Leibniz |
| is dbo:wikiPageDisambiguates of | dbr:TLH dbr:Homogeneity_(disambiguation) |
| is dbo:wikiPageRedirects of | dbr:Transcendental_Law_of_Homogeneity dbr:Law_of_homogeneity |
| is dbo:wikiPageWikiLink of | dbr:Product_rule dbr:Gottfried_Wilhelm_Leibniz dbr:Transcendental_Law_of_Homogeneity dbr:TLH dbr:Adequality dbr:Law_of_continuity dbr:Infinitesimal dbr:Homogeneity_(disambiguation) dbr:Standard_part_function dbr:List_of_things_named_after_Gottfried_Leibniz dbr:Law_of_homogeneity |
| is dbp:notableIdeas of | dbr:Gottfried_Wilhelm_Leibniz |
| is foaf:primaryTopic of | wikipedia-en:Transcendental_law_of_homogeneity |