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Unformatted text preview: FOUNDATIONS OF ANALYSIS SPRING 2008 TRUE/FALSE QUESTIONS THE REAL NUMBERS Chapter #4 (1) Every element in a field has a multiplicative inverse. (2) In a field the additive inverse of 1 is 0. (3) In a field every element has an additive inverse. (4) A field can have two distinct additive identities. (5) For elements of a field, x, y, z , the sum x + y + z is defined by the field axioms. (6) There exists a field containing exactly two elements. (7) In a field containing at least two elements the multiplicative iden- tity is greater than the additive identity. (8) Let x be an element in an ordered field with x > 0. Then x- 1 > 0. (9) Let the field F be ordered by the subset F + and let x, y F . If x > y then x- y F + . (10) Let x, y, z be elements of a field. If xy = xz then y = z . (11) Every subset of an ordered field has a least upper bound in the field. (12) Every non-empty subset of the positive integers contains a great- est lower bound. 1 (13) Let S denote a non-empty subset of an ordered field F that has the least upper bound property. If S has an upper bound in F then S con- tains a least upper bound. (14) Let S denote a non-empty subset of an ordered field F that has the least upper bound property. If S has a lower bound in F then S has a greatest lower bound in F ....
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- Spring '08
- Real Numbers