Axioms (expounded)
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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Closure prop. of Addition | For any a and b in R, the sum a+b is in R.
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Closure prop. of Multiplication | For any a and b in R, the product a・b is in R.
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Associative prop. of Addition | For any a, b, and c in R, (a + b) + c = a + (b + c).
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Associative prop. Multiplication | For any a, b, and c in R, (a ・ b) ・ c = a ・ (b ・ c).
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Commutative prop. of Addition | For any a and b in R, a + b = b + a.
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Commutative prop. of Multiplication | For any a and b in R, a ・ b = b ・ a.
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Distributive prop. of Multiplication over Addition | For any a, b, and c in R, (a + b) ・ c = (a ・ c) + (b ・ c).
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Multiplicative Identity | There is a unique number 1 in R such that for any a in R, a ・ 1 = a.
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Reflexive prop. of Equality | For any a in R, a = a.
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Symmetric prop. of Equality | For any a and b in R, if a = b, then b = a.
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Transitive prop. of Equality | For any a, b, and c in R, if a = b and b = c, then a = c.
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Addition prop. of Equality | For any a, b, and c in R. if a = b, then a + c = b + c.
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Multiplication prop. of Equality | For any a, b, and c in R. if a = b, then a ・ c = b ・ c.
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Created by:
natureworld
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