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section11 - Section 11 Ordered Fields Axioms The set R can...

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Unformatted text preview: Section 11 Ordered Fields Axioms The set R can be described as a complete ordered field. MAT 300 Awtrey MATHEMATICS AND STATISTICS 1 / 28 Section 11 Ordered Fields Axioms The set R can be described as a complete ordered field. Complete means there are no gaps in R . MAT 300 Awtrey MATHEMATICS AND STATISTICS 1 / 28 Section 11 Ordered Fields Axioms The set R can be described as a complete ordered field. Complete means there are no gaps in R . Ordered means that given any two real numbers x and y , either they are equal or one is bigger than the other...we can order the real numbers. MAT 300 Awtrey MATHEMATICS AND STATISTICS 1 / 28 Section 11 Ordered Fields Axioms The set R can be described as a complete ordered field. Complete means there are no gaps in R . Ordered means that given any two real numbers x and y , either they are equal or one is bigger than the other...we can order the real numbers. A field is a set where we can add, subtract, and multiply elements; and if the element is nonzero, we can divide by it. MAT 300 Awtrey MATHEMATICS AND STATISTICS 1 / 28 Section 11 Ordered Fields Axioms The set R can be described as a complete ordered field. Complete means there are no gaps in R . Ordered means that given any two real numbers x and y , either they are equal or one is bigger than the other...we can order the real numbers. A field is a set where we can add, subtract, and multiply elements; and if the element is nonzero, we can divide by it. The goal for this section is to state 15 axioms. MAT 300 Awtrey MATHEMATICS AND STATISTICS 1 / 28 Section 11 Ordered Fields Axioms The set R can be described as a complete ordered field. Complete means there are no gaps in R . Ordered means that given any two real numbers x and y , either they are equal or one is bigger than the other...we can order the real numbers. A field is a set where we can add, subtract, and multiply elements; and if the element is nonzero, we can divide by it. The goal for this section is to state 15 axioms. An axiom is a property that we take as fact, without proving it. MAT 300 Awtrey MATHEMATICS AND STATISTICS 1 / 28 Section 11 Ordered Fields Axioms The set R can be described as a complete ordered field. Complete means there are no gaps in R . Ordered means that given any two real numbers x and y , either they are equal or one is bigger than the other...we can order the real numbers. A field is a set where we can add, subtract, and multiply elements; and if the element is nonzero, we can divide by it....
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This note was uploaded on 02/22/2011 for the course MAT 300 taught by Professor Thieme during the Spring '07 term at ASU.

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section11 - Section 11 Ordered Fields Axioms The set R can...

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