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factors with minus sign
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(Topic)
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The sign (cf. plus sign, opposite number) rule
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derived in the parent entry and concerning numbers and elements  of an arbitrary ring, may be generalised to the following
Theorem. If the sign of one factor in a ring product is changed, the sign of the product changes.
Corollary 1. The product of real numbers is equal to the product of their absolute values equipped with the “ ” sign if the number of negative factors is odd and with “ ” sign if it is even. Especially, any odd power of a negative real number is negative and any even power of it is positive.
Corollary 2. Let us consider natural powers of a ring element. If one changes the sign of the base, then an odd power changes its sign but an even power remains unchanged:
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"factors with minus sign" is owned by pahio.
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(view preamble)
Cross-references: positive, even power, odd power, even, odd, negative, absolute values, real numbers, product, ring product, ring, numbers, opposite number, plus sign
There is 1 reference to this entry.
This is version 3 of factors with minus sign, born on 2007-11-03, modified 2008-06-24.
Object id is 10028, canonical name is FactorsWithMinusSign.
Accessed 524 times total.
Classification:
| AMS MSC: | 13A99 (Commutative rings and algebras :: General commutative ring theory :: Miscellaneous) | | | 97D40 (Mathematics education :: Education and instruction in mathematics :: Teaching methods and classroom techniques. Lesson preparation. Educational principles) |
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Pending Errata and Addenda
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