Lecture Note 3

Question 1

the single, unambiguous idea is called the ________________________ of the
definition

Answer 1

characteristic property

Question 2

it is an argument that is valid and whose premises are
all true

Answer 2

sound argument

Question 3

Around _____________, Euclid organized most of the known mathematics of his time

Answer 3

300 B.C.

Question 4

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

Answer 4

tombstone

Question 5

A model of an axiomatic system can be in the form of a?

Answer 5

diagram

Question 6

it is a logically sound argument that progresses from ideas you accept to the statement you are wondering about

Answer 6

proof

Question 7

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

Answer 7

circular definition

Question 8

a good definition must not be?

Answer 8

circular

Question 9

it is a statement of a single, unambiguous idea that the word, phrase, or symbol being defined represent

Answer 9

definition

Question 10

A __________ for an axiomatic system makes its ideas more realistic

Answer 10

model

Question 11

these are used to form a fundamental vocabulary with which other terms can be defined

Answer 11

undefined (primitive) terms

Question 12

filled-in square at the end of the proof to indicate that the proof is complete

Answer 12

halmos

Question 13

four essential components of axiomatic system:

Answer 13

defined terms, undefined terms, axioms, and theorems

Question 14

two types of undefined terms:

Answer 14

elements and relations

Question 15

As early as _____________, the Greeks began to study the logical connections among mathematical facts

Answer 15

600 B.C.

Question 16

defining a word by simply giving a synonym can lead to a problem of?

Answer 16

circularity

Question 17

defined terms and axioms (rules) are called

Answer 17

theorems

Question 18

A axiomatic system model is an ___________________ if the meanings assigned to the undefined terms are objects and relations adopted from another axiomatic development

Answer 18

Abstract Model

Question 19

it is an interpretation that satisfies all the axioms of the system

Answer 19

model of an axiomatic system

Question 20

two types of axiomatic system models

Answer 20

concrete model and abstract model

Question 21

it is a mixture of
everyday language and strict logic

Answer 21

proof

Question 22

it is any assignment of specific meanings to the undefined terms of that system.

Answer 22

interpretation of an axiomatic system

Question 23

it is the distinctive structure of mathematics.

Answer 23

axiomatic method

Question 24

these are undefined terms that imply relationships between objects

Answer 24

relations

Question 25

From the axiomatic point of view, the undefined terms are implicitly defined by basic propositions that involve these terms. Such propositions are called?

Answer 25

axioms

Question 26

A statement that is derived from the axioms by strict logical proof is called __________.

Answer 26

theorem

Question 27

it form the basis of mathematical proofs that are written in order to establish theorems

Answer 27

axioms

Question 28

A axiomatic system model is a ___________________ if the meanings assigned to the undefined terms are objects and relations adopted from the real world

Answer 28

Concrete Model

Question 29

these are undefined terms that imply objects

Answer 29

elements

Question 30

Q.E.D.

Answer 30

quod erat demonstrandum

Question 31

in mathematics, the rules are called

Answer 31

axioms

Question 32

Sound argument is argument that is ____________ and whose premises are all ____________

Answer 32

valid and true

Question 33

these are statements that are accepted as true without proof

Answer 33

axioms