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# section11 - Section 11 Ordered Fields Axioms The set can be...

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Section 11 – Ordered Fields Axioms The set R can be described as a “complete ordered field.” MAT 300 Awtrey MATHEMATICS AND STATISTICS 1 / 28

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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

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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

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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. The goal for this section is to state 15 axioms. An axiom is a property that we take as fact, without proving it.

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

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