# Chpts_4_S08 - FOUNDATIONS OF ANALYSIS SPRING 2008...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 &gt; 0. Then x- 1 &gt; 0. (9) Let the field F be ordered by the subset F + and let x, y F . If x &gt; 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 ....
View Full Document

## Chpts_4_S08 - FOUNDATIONS OF ANALYSIS SPRING 2008...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online