Remark
5
[20R](Solved on 2022-11-15) Typically
1
you use the notations on the left instead of the writings on the right (where \(x,y,z\) are in the field and \(n\) is positive integer)
|
\(x-y\) |
\(x+ (-y)\) |
|
\(\frac{x} y\) |
\(x ⋅ y^{-1}\) |
|
\(x+y+z\) |
\((x+y)+x\) |
|
\(x y z\) |
\((x⋅ y)⋅ z\) |
|
\(n x\) |
\(\underbrace{x+ \ldots +x}_{n~ \hbox{times}}\) |
|
\(x^ n\) |
\(\underbrace{x⋅ \ldots ⋅ x}_{n~ \hbox{times}}\) |
|
\(x^{-n}\) |
\((x^{-1}) ^ n\) |
Precisely, \(n x\) means ”add \(x\) to itself \(n\) times”; the operation \(n↦ n⋅ x\) can be defined recursively setting \(0⋅ x=0\) and \((n+1)⋅ x= n⋅ x + x\). Similarly \(x^ n\) means ”multiply \(x\) by itself \(n\) times”: see the exercise [202].