I wanted to ask what are field and field axioms? I have tried looking on Wikipedia and Wolfram But They are too are advanced and I cant a understand one bit.So please any help would be much appreciated. Also there is a question in my book :"What is the difference between Real and the Complex fields?" As I don't know anything about fields ,so I don't know the answer too and cant think of one as well ( as I repeat I don't know anything about fields),So please again any help would be much appreciated on understanding Fields and field axioms.
THANKS VERY MUCH
Answer
A field is a set of numbers which satisfy some calculation rules. For the field the following rules hold:
Addition rules
- Addition has the neutral element 0
- Addition has an inverse (adding the negative part to a number)
- Addition is associative
Multiplication rules
- Multiplication has the neutral element 1
- Multiplication is always invertible (by division)
Multiplication is associative
And another important fact is that the distributive law holds!
Real fields are fields of real numbers while complex fields consist on complex numbers.
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