Different Conceptions of Z - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-18T11:35:01Z http://mathoverflow.net/feeds/question/12613 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/12613/different-conceptions-of-z Different Conceptions of Z Nick Salter 2010-01-22T07:13:56Z 2010-01-22T15:54:01Z <p>To the algebraist, \$\mathbb{Z}\$ is just the free group with one generator. To the algebraic topologist, \$\mathbb{Z}\$ is just the fundamental group of the circle. To be glib, what do \$\mathbb{Z}\$ mean to you?</p> http://mathoverflow.net/questions/12613/different-conceptions-of-z/12614#12614 Answer by Kevin Lin for Different Conceptions of Z Kevin Lin 2010-01-22T07:20:10Z 2010-01-22T07:20:10Z <p>Initial object in the category of commutative rings.</p> http://mathoverflow.net/questions/12613/different-conceptions-of-z/12617#12617 Answer by Ilya Grigoriev for Different Conceptions of Z Ilya Grigoriev 2010-01-22T07:25:10Z 2010-01-22T07:25:10Z <p>To a number theorist, shouldn't \$\mathbb Z\$ be the world? </p> http://mathoverflow.net/questions/12613/different-conceptions-of-z/12619#12619 Answer by Joel Dodge for Different Conceptions of Z Joel Dodge 2010-01-22T08:24:56Z 2010-01-22T08:24:56Z <p>Final object in the category of schemes.</p> http://mathoverflow.net/questions/12613/different-conceptions-of-z/12645#12645 Answer by Johannes Hahn for Different Conceptions of Z Johannes Hahn 2010-01-22T15:37:34Z 2010-01-22T15:37:34Z <p>Just \$\mathbb{Z}\$ ? ;-)</p> http://mathoverflow.net/questions/12613/different-conceptions-of-z/12649#12649 Answer by Tom LaGatta for Different Conceptions of Z Tom LaGatta 2010-01-22T15:54:01Z 2010-01-22T15:54:01Z <p>An infinite discrete subset of \$\mathbb R\$.</p>