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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


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".



