Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Galileos_paradox> ?p ?o }
Showing triples 1 to 46 of
46
with 100 triples per page.
- Galileos_paradox abstract "Galileo's paradox is a demonstration of one of the surprising properties of infinite sets. The ideas were not new with him, but his name has come to be associated with them. In his final scientific work, Two New Sciences, Galileo Galilei made apparently contradictory statements about the positive integers. First, some numbers are squares, while others are not; therefore, all the numbers, including both squares and non-squares, must be more numerous than just the squares. And yet, for every square there is exactly one positive number that is its square root, and for every number there is exactly one square; hence, there cannot be more of one than of the other. This is an early use, though not the first, of the idea of one-to-one correspondence in the context of infinite sets.Galileo concluded that the ideas of less, equal, and greater apply to (what we would now call) finite sets, but not to infinite sets. In the nineteenth century Cantor said that this restriction is not necessary. It is possible to define comparisons amongst infinite sets in a meaningful way (by which definition the two sets he considers, integers and squares, have \"the same size\"), and that by this definition some infinite sets are strictly larger than others. Galileo also worked on Zeno's paradoxes in order to open the way for his mathematical theory of motion.".
- Galileos_paradox wikiPageExternalLink 00004276.
- Galileos_paradox wikiPageID "339195".
- Galileos_paradox wikiPageLength "6589".
- Galileos_paradox wikiPageOutDegree "17".
- Galileos_paradox wikiPageRevisionID "674499264".
- Galileos_paradox wikiPageWikiLink Bijection.
- Galileos_paradox wikiPageWikiLink Cantors_diagonal_argument.
- Galileos_paradox wikiPageWikiLink Cardinality.
- Galileos_paradox wikiPageWikiLink Category:Paradoxes_of_infinity.
- Galileos_paradox wikiPageWikiLink Category:Paradoxes_of_set_theory.
- Galileos_paradox wikiPageWikiLink Finite_set.
- Galileos_paradox wikiPageWikiLink Galileo_Galilei.
- Galileos_paradox wikiPageWikiLink Georg_Cantor.
- Galileos_paradox wikiPageWikiLink Hilberts_paradox_of_the_Grand_Hotel.
- Galileos_paradox wikiPageWikiLink Infinite_set.
- Galileos_paradox wikiPageWikiLink Matthew_W._Parker.
- Galileos_paradox wikiPageWikiLink Natural_number.
- Galileos_paradox wikiPageWikiLink Square_number.
- Galileos_paradox wikiPageWikiLink Square_root.
- Galileos_paradox wikiPageWikiLink Two_New_Sciences.
- Galileos_paradox wikiPageWikiLink Zeno_of_Elea.
- Galileos_paradox wikiPageWikiLinkText "Galileo's paradox".
- Galileos_paradox wikiPageUsesTemplate Template:Quotation.
- Galileos_paradox wikiPageUsesTemplate Template:Reflist.
- Galileos_paradox subject Category:Paradoxes_of_infinity.
- Galileos_paradox subject Category:Paradoxes_of_set_theory.
- Galileos_paradox hypernym Demonstration.
- Galileos_paradox type ArtificialSatellite.
- Galileos_paradox type Concept.
- Galileos_paradox comment "Galileo's paradox is a demonstration of one of the surprising properties of infinite sets. The ideas were not new with him, but his name has come to be associated with them. In his final scientific work, Two New Sciences, Galileo Galilei made apparently contradictory statements about the positive integers. First, some numbers are squares, while others are not; therefore, all the numbers, including both squares and non-squares, must be more numerous than just the squares.".
- Galileos_paradox label "Galileo's paradox".
- Galileos_paradox sameAs Q2915190.
- Galileos_paradox sameAs Парадокс_на_Галилей.
- Galileos_paradox sameAs Galileis_Paradoxon.
- Galileos_paradox sameAs Paradoja_de_Galileo.
- Galileos_paradox sameAs Galilein_paradoksi.
- Galileos_paradox sameAs הפרדוקס_של_גלילאו.
- Galileos_paradox sameAs Paradox_van_Galilei.
- Galileos_paradox sameAs Paradòss_ëd_Galilei.
- Galileos_paradox sameAs Paradoxo_de_Galileu.
- Galileos_paradox sameAs m.01xw8_.
- Galileos_paradox sameAs Парадокс_Галилея.
- Galileos_paradox sameAs Q2915190.
- Galileos_paradox wasDerivedFrom Galileos_paradox?oldid=674499264.
- Galileos_paradox isPrimaryTopicOf Galileos_paradox.