"Dik T. Winter" wrote...
....
When you look at the definition for rings, and stuff like that, you will
find that they are very different. If you look you will find that
a - b
is just shorthand for
a + b'.
where b' is the negative of b. So
0 - 5^2
is shorthand for
0 + (5^2)'
....

I don't recall exponentiation being covered in the development of either
rings or fields. Just addition and multiplication and their respective
inverses. Exponentiation wasn't brought up until polynomials were
introduced.

Also, you're now arguing for both interpretations. If 5^2 = 25, 0 + (5^2)' =
0 + (25)' = 25' = -25 rather than 25. That's the nub of this whole argument.



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