Comments on: Why are the Integers a Cyclic Group?
http://cafe.elharo.com/math/why-are-the-integers-a-cyclic-group/
Longer than a blog; shorter than a bookSun, 14 May 2023 05:42:10 +0000hourly1https://wordpress.org/?v=4.9.20By: M UBAID ULLAH
http://cafe.elharo.com/math/why-are-the-integers-a-cyclic-group/comment-page-1/#comment-4472407
Sat, 26 Nov 2016 13:53:10 +0000http://cafe.elharo.com/?p=733#comment-4472407how can we generate the 0 and the negative elements from 1?
]]>By: M UBAID ULLAH
http://cafe.elharo.com/math/why-are-the-integers-a-cyclic-group/comment-page-1/#comment-4472405
Sat, 26 Nov 2016 13:50:28 +0000http://cafe.elharo.com/?p=733#comment-4472405please use an example to explain that set of intigers can b generate by 1
]]>By: John Cowan
http://cafe.elharo.com/math/why-are-the-integers-a-cyclic-group/comment-page-1/#comment-1040104
Sun, 27 May 2012 18:53:57 +0000http://cafe.elharo.com/?p=733#comment-1040104In the early development of mathematical theories, it’s typical to look only at finite sets, and the intuitions (and names) that develop during that stage don’t necessarily apply cleanly to infinite sets. In any finite integral domain, it’s clear that the members of {x | x = 2n} are only about half the domain, but in the integers themselves, the even integers and the integers have exactly the same size. This is counterintuitive but leads to the best overall results. Similarly, treating the integers (and groups isomorphic to them) as cyclic groups gives the best generalizations.
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