Cauchy sequence, DYK Fact #165
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Cauchy sequence, DYK Fact #165| algebraic topology |
Posted: 15:10 Friday 30 March 2007
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Renaissance  Group: Friends Posts: 143 Member No.: 14 Joined: 20 Feb 2007  |
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| JaneFairfax |
Posted: 20:38 Thursday 05 February 2009
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 The Enlightenment Group: Moderators Posts: 673 Member No.: 20 Joined: 03 Mar 2007 |
Did you know? Cauchy sequences of rational numbers can be added and multiplied term by term, and the results are also Cauchy sequences of rataional numbers. Indeed, under these operations, the set |
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| algebraic topology |
Posted: 10:41 Friday 06 February 2009
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Renaissance Group: Friends Posts: 143 Member No.: 14 Joined: 20 Feb 2007 |
Did you know? The elements of |
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| JaneFairfax |
Posted: 14:01 Friday 06 February 2009
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The Enlightenment Group: Moderators Posts: 673 Member No.: 20 Joined: 03 Mar 2007 |
Did you know? Cauchy sequences of rational numbers provide one of two principal methods of constructing the real numbers from the rational numbers. The other method, which I read about in A Survey of Modern Algebra by Garrett Birkhoff and Saunders MacLane a long time ago, is by means of Dedekind cuts. |
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| algebraic topology |
Posted: 16:34 Friday 06 February 2009
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Renaissance Group: Friends Posts: 143 Member No.: 14 Joined: 20 Feb 2007 |
Did you know? The construction of the reals from the rationals (whether by Cauchy sequences or by Dedekind cuts) involves the creation of a complete ordered field. |
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| JaneFairfax |
Posted: 18:12 Friday 06 February 2009
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The Enlightenment Group: Moderators Posts: 673 Member No.: 20 Joined: 03 Mar 2007 |
Did you know? Birkhoff & MacLane’s book also gives a proof of the result that any two complete ordered fields are isomorphic. |
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| algebraic topology |
Posted: 01:11 Wednesday 11 February 2009
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Renaissance Group: Friends Posts: 143 Member No.: 14 Joined: 20 Feb 2007 |
Did you know? Cauchy sequences are named after the French mathematician Augustin Louis Cauchy. |
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| JaneFairfax |
Posted: 16:30 Wednesday 11 February 2009
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The Enlightenment Group: Moderators Posts: 673 Member No.: 20 Joined: 03 Mar 2007 |
Did you know? Dedekind cuts are named after the German mathematician Richard Dedekind. |
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Moreover, the set 
