Intro to Logic

Question 1

What does it mean that proposition one logically follows from the axioms?

Answer 1

It means that it is impossible for the axioms to be true and the propositions to be false

Question 2

Who was Euclid?

Answer 2

Euclid was an ancient Greek mathematician active as a geometer and logician. Considered the “father of geometry”, he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century.

Question 3

What is a point?

Answer 3

that which has no part

Question 4

What is a line?

Answer 4

A length without breadth

Question 5

what is a straight line?

Answer 5

A line that stays within 2 points

Question 6

What is Pi?

Answer 6

The number π is a mathematical constant that is the ratio of a circle’s circumference to its diameter, approximately equal to 3.14159

Question 7

Well-ordering

Answer 7

Every non-empty subset S of A has a smaller member

Question 8

totality

Answer 8

a<b>a, whenever a and b are distinct objects</b>

Question 9

transitivity

Answer 9

if a<b and b<c then a<c

Question 10

asymmetry

Answer 10

if a<b then not b<a

Question 11

transitive

Answer 11

for any a, b, c = A if aRb and bRc, then aRc

Question 12

Cantor’s Theorum

Answer 12

the theorem that the cardinality (numerical size) of a set is strictly less than the cardinality of its power set, or collection of subsets

Question 13

What is “S”?

Answer 13

the set of the bijection of f

Question 14

what is bijection?

Answer 14

a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set