Can someone please give me the definition of finite fields? (A defenition that gives me all finite fields, not something like "all finite fields are finite")
And PLEASE dont copy paste from wikipedia, i just started linear algebra.
Im counting on you alan!
A field is an algebraic structure with certain properties.
It is a set of mathematical objects on which are defined two binary operations, namely addition and multiplication.
The operations are commutative (e.g. x*y = y*x) and associative (e.g. (x+y)+z = x+(y+z)) and have identity elements (e.g. 0 for addition and 1 for multiplication).
They have inverse elements (e.g. x and -x for addition; x and 1/x for multiplication). Multiplication is distributive over addition (i.e. x*(y+z) = x*y + x*z).
A finite field is a set with these properties, but it only has a finite number of elements.
Hope this helps!