Lecture 1

Question 1

Algebra

Answer 1

The study of structures on sets

Question 2

Structure

Answer 2

Thick of as an operation. Such as addition or multiplication

Question 3

Binary operation

Answer 3

Let S be a set, a binary operation on S is a map. For Z both + and * are binary operations where are / is not.

Question 4

Well-ordering principle

Answer 4

If set S subsets Z and S is bounded below, then S has a minimal element. This is not true for Q.

Question 5

a|b

Answer 5

a divides b if there is an integer c s.t. ac=b

Question 6

Fact 3 (idk what it’s called)

Answer 6

For any numbers a, b there is a unique non-negative number d, s.t. d|a and d|b

Question 7

Greatest common divisor (GCD)

Answer 7

If c|a and c|b then c|d and d = gcd(a,b)

Question 8

Least common multiple (LCD)

Answer 8

If a, b are in Z, there is a unique non-negative integer l s.t.
1. a|l and b|l
2. If a|m and b|m then l|m