Axiomatic Structure of Mathematical system Flashcards
(26 cards)
It is a statement or proposition which is regarded as being established, accepted, or self-evidently true.
Axiom
It refers to the proper fundamental ideas of Mathematics that are regarded as being established and accepted in daily life.
Axiomatic Structure of Mathematics
It is the study of different types of shapes, figures, and sizes in Mathematics or in real life.
Geometry
The word “Geo” means ___.
Earth
The word “Metry” means ___.
Measurement
These are terms that we cannot precisely define but are accepted by their definition.
Undefined Terms
These are terms that have formal definitions and are used to define mathematical concepts.
Defined Terms
It is a statement that is accepted as true without proof and can be used as a reason in proving mathematical statements.
Axiom/Postulate
It is a statement that can be proven, and once proven, it can be used as a reason in proving other statements.
Theorem
It is a position in space with no length, width, thickness, or dimensions, named with a capital letter and represented by a dot.
Point
It is a set of infinite points extending in two directions with no thickness, labeled with two capital letters.
Line
It is a flat surface or figure that has length and width but no thickness, named by a single capital letter or by any three points that are not on the same line.
Plane
These are points that belong to the same line.
Collinear Points
These are points that do not belong to the same line.
Non-Collinear Points
These are points that belong to the same plane.
Coplanar Points
These are points that do not belong to the same plane.
Non-Coplanar Points
It is a part of a line that has two endpoints and all points in between.
Line Segment
It is a part of a line that has one endpoint and extends in one direction.
Ray
These are rays with a common endpoint but extending in opposite directions.
Opposite Rays
Collinear points are points that ___.
Lie on the same line
Undefined terms are accepted without proof and serve as ___.
The fundamental building blocks in geometry
A ray consists of infinitely many points and extends ___.
Indefinitely in one direction
A plane is comprised of ___.
Infinitely many points
Postulates are accepted without proof and are used as ___.
Foundational principles in logical reasoning
