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Topic: Re: In "square root of -1", should we say "minus 1" or "negative
1"?

Replies: 1   Last Post: Dec 4, 2012 9:58 AM

 Messages: [ Previous | Next ]
 Paul A. Tanner III Posts: 5,920 Registered: 12/6/04
Re: In "square root of -1", should we say "minus 1" or "negative 1"?
Posted: Dec 4, 2012 2:25 AM

On Tue, Dec 4, 2012 at 12:08 AM, Joe Niederberger <niederberger@comcast.net> wrote:
>>And so to say that that the theorem itself (and not merely such a particular proof of it) is based on such is not right.
>
> I said the sign rule for multiplying negative integers is not based on the fact that integers have a magnitude (together with a sign.) You think it is?
>
> Joe N

You said:

"In fact it emphasizes the fact the rule is based on the signs alone."

This is not correct.

I said :

"One of the standard proofs in abstract algebra textbooks of the theorem (-a)(-b) = ab for all ring elements a,b (including for rings that are not ordered) contains the equality (-a)(-b) = -(-(ab)).

Is this what you meant?

Regardless, there are ways to prove this theorem that does not use the prior theorem of additive groups x = -(-x).

And so to say that that the theorem itself (and not merely such a particular proof of it) is based on such is not right."

That is, the theorem (-a)(-b) = ab is about the elements of the sets and the unary function of taking additive inverses of elements, not about "the signs", which is about how to write "the additive inverse of".

Date Subject Author
12/4/12 Joe Niederberger
12/4/12 Paul A. Tanner III