I've been wanting to catch back up on my physics and math. I was looking into equations on E&M, which led me to electric fields, which led me through differentiation, and on.(adsbygoogle = window.adsbygoogle || []).push({});

I am looking up on Wikipedia what a mathematical field is. Well, it's an algebraic structure. It's also a ring. A ring has more structure than an abelian group, but less than a field. A field is not just a ring, but a commutative division ring.

And so on. Now we have structures, fields, rings, abelian groups, and properties of commutativity to them.

I feel I'm going in circles. I just want to know what a field is, and if it's the same as a magnetic/electric field. How can I grasp this abstract math? My brain can't seem to grasp it.

I know a set is a group of numbers, like {1,2,3}

I guess this could be a 1x3 matrix too, and in computers it's an array.

How can this object called a "set" be represented as a field, structure, ring, abelian group, etc?

Isn't a field like a 2d or 3d (or n-dimensional) surface of points?

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