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- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/00%3A_Front_Matter
- https://math.libretexts.org/Bookshelves/Geometry/An_IBL_Introduction_to_Geometries_(Mark_Fitch)/zz%3A_Back_Matter/20%3A_GlossaryExample and Directions Words (or words that have the same definition) The definition is case sensitive (Optional) Image to display with the definition [Not displayed in Glossary, only in pop-up on pag...Example and Directions Words (or words that have the same definition) The definition is case sensitive (Optional) Image to display with the definition [Not displayed in Glossary, only in pop-up on pages] (Optional) Caption for Image (Optional) External or Internal Link (Optional) Source for Definition "Genetic, Hereditary, DNA ...") (Eg. "Relating to genes or heredity") The infamous double helix CC-BY-SA; Delmar Larsen Glossary Entries Definition Image Sample Word 1 Sample Definition 1
- https://math.libretexts.org/Bookshelves/Geometry/An_IBL_Introduction_to_Geometries_(Mark_Fitch)/01%3A_Completeness_and_Consistency/1.3%3A_ConsistencyDefinition: Five Point Geometry Use the following axioms and definitions of intersection and parallel as a definition of the five point geometry. There exist exactly five points. There exist exactly f...Definition: Five Point Geometry Use the following axioms and definitions of intersection and parallel as a definition of the five point geometry. There exist exactly five points. There exist exactly five lines. Any two distinct points have exactly one line on both of them. Each line is on exactly two points. Explore the five point geometry as follows. Draw five points using Geogebra. Use Axiom 3 to draw all required lines. How many lines did you construct? Compare this answer to Axiom 2.
- https://math.libretexts.org/Bookshelves/Geometry/An_IBL_Introduction_to_Geometries_(Mark_Fitch)/05%3A_Hyperbolic_Geometry
- https://math.libretexts.org/Bookshelves/Geometry/An_IBL_Introduction_to_Geometries_(Mark_Fitch)/02%3A_Neutral_Geometry
- https://math.libretexts.org/Bookshelves/Geometry/An_IBL_Introduction_to_Geometries_(Mark_Fitch)/03%3A_Synthetic_Euclidean_Geometry/3.04%3A_New_PageFor each construction figure out how to do it using the classic Greek tools: a straight edge and rusty compass (okay that isn't quite classic Greek). Construct an equilateral triangle with side length...For each construction figure out how to do it using the classic Greek tools: a straight edge and rusty compass (okay that isn't quite classic Greek). Construct an equilateral triangle with side length matching a given segment. Given a line segment construct the perpendicular bisector of it. Construct a square with side length matching a given segment. Construct the midpoint of a line segment. Construct a line parallel to a given line through a given point.
- https://math.libretexts.org/Bookshelves/Geometry/An_IBL_Introduction_to_Geometries_(Mark_Fitch)/zz%3A_Back_Matter
- https://math.libretexts.org/Bookshelves/Geometry/An_IBL_Introduction_to_Geometries_(Mark_Fitch)/06%3A_Projective_Geometry/6.02%3A_New_PageA transformation is a perspectivity if and only if it maps the points of a line to the points of another line such that all lines from points to their images are incident in a single point. Choose thr...A transformation is a perspectivity if and only if it maps the points of a line to the points of another line such that all lines from points to their images are incident in a single point. Choose three points on one of the lines and find the points on the second line to which they are mapped by the perspectivity defined by your chosen point. Two triangles are perspective with respect to a point if and only if the lines connecting corresponding pairs of vertices are incident in a point.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/04%3A_Relations/4.05%3A_Combinatorics-_Inclusion_ExclusionThis page explains the inclusion-exclusion principle for counting distinct elements in overlapping sets, detailing how to adjust for over-counting overlaps. An example with students in math courses il...This page explains the inclusion-exclusion principle for counting distinct elements in overlapping sets, detailing how to adjust for over-counting overlaps. An example with students in math courses illustrates this principle. It also defines a derangement as a permutation where no element retains its original position, and concludes with practice checkpoints on related counting problems.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/04%3A_Relations/4.04%3A_Partially_Ordered_SetsThis page defines partially ordered sets (posets) and their properties like reflexivity, anti-symmetry, and transitivity. It explains representation through Hasse diagrams and illustrates examples suc...This page defines partially ordered sets (posets) and their properties like reflexivity, anti-symmetry, and transitivity. It explains representation through Hasse diagrams and illustrates examples such as numeric divisibility and subset relations. Key terms related to posets, including comparable elements, total ordering, and lattices, are defined, alongside practical checkpoints for assessing poset properties and constructing Hasse diagrams.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/02%3A_Logic/2.03%3A_Predicate_LogicThis page covers the use of predicates and quantifiers in logic for effective communication, including negation and application through exercises. It provides examples involving bees, flowers, trees, ...This page covers the use of predicates and quantifiers in logic for effective communication, including negation and application through exercises. It provides examples involving bees, flowers, trees, and moose, highlighting logical equivalences and implications related to these subjects. The text encourages readers to translate natural language statements into logical notation and practice negation and interpretation, reinforcing their understanding of predicate logic in various scenarios.
