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Re: In "square root of -1", should we say "minus 1" or "negative 1"?
Posted:
Dec 3, 2012 12:55 PM
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On Sun, Dec 2, 2012 at 11:10 PM, Jonathan Crabtree <sendtojonathan@yahoo.com.au> wrote:
...
> Modern mathematicians are so sloppy. They 'dumb down' a radio show (NPR) or tv show (BBC) because minus is a simpler word than negative.
>
> They dumb down book titles and use minus instead of negative so they get published.
>
This is very wrong. Please read my post
"In "square root of -1", should we say "minus 1" or "negative 1"?"
http://mathforum.org/kb/message.jspa?messageID=7930876
to see that the term "minus" is not used as a simpler term than "negative" but is instead used as a simpler term for "the additive inverse of".
Yes, in ordered sets, the terms "minus" and "negative" can be exchanged in denoting the additive inverse of an element, since, as I pointed out, "negative" and "positive" are essentially defined in only ordered set contexts, meaning "less than 0" and "greater than 0". But in sets that are not ordered - like complex numbers in which only the real subset is ordered, the term "negative" can apply only to those elements in the real subset.
That is, "minus 1 " and "negative 1" are OK in the real numbers, but for complex numbers that are not real numbers like i, "negative i" is not right - only "minus i" is OK, since -i is not less than 0 and is not greater than 0 and is not equal to 0 as well. You have to redefine "negative" contrary to how it is defined in abstract algebra. See
http://en.wikipedia.org/wiki/Ordered_ring
for more on this about the terms "positive" and "negative".
So mathematicians are not being sloppy when they say "minus x" for "the additive inverse of x" - they are covering all contexts of whether the element x is contained in an ordered set, they are using the only universal term for "the additive inverse of", which is "minus".
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