Please help - Difference between Finite Set and Finite Field
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From: deepakc on 13 Feb 2010 07:38 Hi, Could someone please help me understand the difference between the terms "Finite Set" and "Finite Field"? I understand that "Finite Set" is a set with a finite number of elements. I also understand roughly that a "Finite Field" is something similar. But I do not get the difference between them? Please help. Thanks, -Deepak
From: Jym on 13 Feb 2010 08:46 On Sat, 13 Feb 2010 13:38:42 +0100, deepakc <deepakc(a)pmail.ntu.edu.sg> wrote: > Hi, > > Could someone please help me understand the difference between the > terms "Finite Set" and "Finite Field"? > > I understand that "Finite Set" is a set with a finite number of > elements. I also understand roughly that a "Finite Field" is something > similar. > > But I do not get the difference between them? I guess the finite field is a field in addition to being a finite set... A field is an algebraic structure while a set is just a collection of objects. A field is required to have two internal laws ("addition" and "multiplication") with some properties on them (associativity, commutativity, neutral element, distributivity). For details, see: http://en.wikipedia.org/wiki/Field_(mathematics) -- Hypocoristiquement, Jym.
From: Kaz Kylheku on 13 Feb 2010 12:29 On 2010-02-13, deepakc <deepakc(a)pmail.ntu.edu.sg> wrote: > But I do not get the difference between them? A set is an unordered collection of distinct objects. A set indicates whether or not some element is its member. A field is a tuple consisting of a set of elements, two binary operations, and two special elements from the set. Furthermore, the field must satisfy certain axioms. So as you can see, the two are quite different even at the basic structural level, since a tuple is ordered, whereas a set isn't.
From: deepakc on 13 Feb 2010 12:54
On Feb 13, 5:29 pm, Kaz Kylheku <kkylh...(a)gmail.com> wrote: > On 2010-02-13, deepakc <deep...(a)pmail.ntu.edu.sg> wrote: > > > But I do not get the difference between them? > > A set is an unordered collection of distinct objects. A set indicates > whether or not some element is its member. > > A field is a tuple consisting of a set of elements, two binary > operations, and two special elements from the set. Furthermore, the > field must satisfy certain axioms. > > So as you can see, the two are quite different even at the basic > structural level, since a tuple is ordered, whereas a set isn't. Hi Jym and Kaz, Thanks for both your posts. That was very helpful. -Deepak |