Lecture Note 3 Flashcards
the single, unambiguous idea is called the ________________________ of the
definition
characteristic property
it is an argument that is valid and whose premises are
all true
sound argument
Around _____________, Euclid organized most of the known mathematics of his time
300 B.C.
Sometimes they place a small rectangle with its shorter side horizontal, meaning the death of suspicion of the validity of the statement that was to be proved
tombstone
A model of an axiomatic system can be in the form of a?
diagram
it is a logically sound argument that progresses from ideas you accept to the statement you are wondering about
proof
it is a type of definition where its defining condition
either uses the term itself or uses terms that are themselves defined using
the term being defined
circular definition
a good definition must not be?
circular
it is a statement of a single, unambiguous idea that the word, phrase, or symbol being defined represent
definition
A __________ for an axiomatic system makes its ideas more realistic
model
these are used to form a fundamental vocabulary with which other terms can be defined
undefined (primitive) terms
filled-in square at the end of the proof to indicate that the proof is complete
halmos
four essential components of axiomatic system:
defined terms, undefined terms, axioms, and theorems
two types of undefined terms:
elements and relations
As early as _____________, the Greeks began to study the logical connections among mathematical facts
600 B.C.
defining a word by simply giving a synonym can lead to a problem of?
circularity
defined terms and axioms (rules) are called
theorems
A axiomatic system model is an ___________________ if the meanings assigned to the undefined terms are objects and relations adopted from another axiomatic development
Abstract Model
it is an interpretation that satisfies all the axioms of the system
model of an axiomatic system
two types of axiomatic system models
concrete model and abstract model
it is a mixture of
everyday language and strict logic
proof
it is any assignment of specific meanings to the undefined terms of that system.
interpretation of an axiomatic system
it is the distinctive structure of mathematics.
axiomatic method
these are undefined terms that imply relationships between objects
relations
From the axiomatic point of view, the undefined terms are implicitly defined by basic propositions that involve these terms. Such propositions are called?
axioms
A statement that is derived from the axioms by strict logical proof is called
__________.
theorem
it form the basis of mathematical proofs that are written in order to establish theorems
axioms
A axiomatic system model is a ___________________ if the meanings assigned to the undefined terms are objects and relations adopted from the real world
Concrete Model
these are undefined terms that imply objects
elements
Q.E.D.
quod erat demonstrandum
in mathematics, the rules are called
axioms
Sound argument is argument that is ____________ and whose premises are
all ____________
valid and true
these are statements that are accepted as true without proof
axioms
