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Constructible universe

Geometry Theorems and Postulates for a Midterm

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Geometry
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Mathematics
Elementary geometry
Distance
Length
Axiom
Constructible universe
Line segment
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midterm geometry notes

DEFINITIONS?Def. line segment (segment) - part of a line that has 2 definite endpoints?Def. ray - part of a line that starts with a definite endpoint and extends indefinitely in 1 direction?Def. angle - the union of 2 noncollinear rays with a common endpoint?Def. union - elements belonging in 1 or both sets?Def. intersection - elements that belong to both sets?Def. absolute value - |x| = if x _>_ 0; -x if x _<_ 0?Def. segment length - the distance between the endpoints?Def. congruent segments - segments with the same length?Def. midpoint - a point B is called the midpoint of lineAC if A - B - C and AB = BC?Def. segment bisector - a point, line, ray, segment, or plane that passes through the midpoint of a line?Def.

Algebra 2

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Algebra
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Abstract algebra
Mathematics
General topology
Algebra
Closure
World Wide Web
Integer
Constructible universe
Closed set
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math
. A subset of the real numbers is closed under addition if, for any two numbers, a and b, that are members of the subset, the number is also a member of the subset. Tell whether each of the following subsets of the real numbers is closed under addition. If it is not, give an example that shows it is not. a. The set of whole numbers b. The set of negative integers c. The set of irrational numbers d. The set of rational numbers 2. For each of the sets in Problem 1, tell whether the set is closed under multiplication. If it is not, give an example that shows it is not. 3. a. For each of the following pairs of rational numbers, and find the rational number and write the 3 rational numbers in increasing order. (i) (ii) (iii) (iv)
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