Why Is y − 1 ?

Question

Why Is       y          −      1      ?

luisjoseblash2 · Accepted Answer

If you want to understand these fundamentals and the book you are reading is asking you to just believe this or that 'fact', then just get rid of the book and find a good one. You are not supposed to just believe anything. There are plenty of books that will prove the fundamental results as well. Look for introductory books on analysis and/or algebra (not pre-calc or pre-algebra) and enjoy!
For now:

(- 1) (- 1) + (- 1) = (- 1) \cdot ((- 1) + 1)

by distributivity. Then

(- 1) \cdot ((- 1) + 1) = (- 1) \cdot 0 = 0

(but now you may want to know why

a \cdot 0 = 0

As for

y^{- 1}

, that is just defined, for

y \neq 0

to be

1 / y

. The reason is that it agrees with the familiar rules for exponentiation, so there is nothing arbitrary in this definition either.

sedeln5w · Accepted Answer

For   y  ≠  0 , by using the factorization and simplifying rules we have       y    y    =      1    y    ×  y  =  1. . By multiplying both side of this equation from the right hand side by       y          −      1       we do have       1    y    ×  y  ×      y          −      1        =  1  ×      y          −      1      Where the last results came from the multiplication rule for exponentials; i.e.       x                  y        1              ×      x                  y        2              =      x                  y        1            +              y        2            . And we are done.

Why Is y

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