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• 13:10, 16 October 2026 Rongzhou talk contribs created page Field (mathematical concept) (Created page with "A '''field''' is a set closed under two binary operations, with some special properties by definition. == Formal definition == Let $F:|F| \ge 2$ be a set, and $+,\cdot$ two binary operations defined over $F$. If $\forall a,b,c \in F$: * $a+b=b+a;a \cdot b = b \cdot a$ ('''commutativity''') * $(a+b)+c=a+(b+c);(a \cdot b)\cdot c = a \cdot (b \cdot c)$ ('''associativity''') * $\exists 0_F,1_F \in F: a+0_F=a, a \cdot 1_F=a$ ('''identity''') * $\e...")