I have a set of numbers, how do I go about proving they form a field

by andrey21
Tags: field, form, numbers, proving
andrey21 is offline
Feb24-11, 11:10 AM
P: 466
I have a set of numbers, how do I go about proving they form a field

Heres what I know

It has to be commutative under addition, which should give symmetry down the leading diagonal, which it does. What else must I show??

Thanks in advance
Phys.Org News Partner Science news on Phys.org
Going nuts? Turkey looks to pistachios to heat new eco-city
Space-tested fluid flow concept advances infectious disease diagnoses
SpaceX launches supplies to space station (Update)
HallsofIvy is online now
Feb24-11, 11:21 AM
Sci Advisor
PF Gold
P: 38,882
I don't quite understand what you are talking about. A "set of numbers"? That doesn't form a field- a single set is not a field. A field is a set of objects (which might or might not be numbers) together with two binary operations called "+" and "*". They must satisfy several laws:
1) They form a commutative group with addition (so, yes, commutative under addition but also associative, there exist an additive identity (0), and every member has an additive inverse.
2) Multiplication is commutative and associative and the distributive law holds. There is a multiplicative identity land every element except 0 (the additive identity) has a multiplicative inverse.

I have no idea what you mean by "symmetry down the leading diagonal". Are you referring to a diagonal in the additive or multiplcative tables? If so, that is just saying "commutative" again.
andrey21 is offline
Feb24-11, 11:25 AM
P: 466
Yes sorry I didn't word the question very well. I do have two tables for "+" and "*". In the + table is does have symmetry down the leading diagonal, so that is commutative. There does exist a zero, what do you mean by additive inverse?

Register to reply

Related Discussions
Proving that (Even Numbers)^n = Even Numbers Calculus & Beyond Homework 8
Prime numbers of given form Linear & Abstract Algebra 7
Polar form of complex numbers Calculus & Beyond Homework 2
Proving a Bijection with Catalan Numbers Set Theory, Logic, Probability, Statistics 0
Proving a property of real numbers Calculus & Beyond Homework 10