Cardinals and the size of infinite sets 1 Review of bijections
... Definition 6 A set A is called countable if either it is finite or there is a bijection N → A. (Sometimes a countable set that is not finite is called infinite countable.) The idea of this definition is that for a countable set you can write out the elements of A in order as a1 , a2 , a3 , . . . , w ...
... Definition 6 A set A is called countable if either it is finite or there is a bijection N → A. (Sometimes a countable set that is not finite is called infinite countable.) The idea of this definition is that for a countable set you can write out the elements of A in order as a1 , a2 , a3 , . . . , w ...
Logic, Sets, and Proofs
... Often we are working with elements of a fixed set. In calculus, this fixed set is often the real numbers R or an interval [a, b] ⊆ R. In linear algebra, the fixed set is often Rn , Cn or an abstract vector space V (all of these terms will eventually be defined). In the discussion that follows, this ...
... Often we are working with elements of a fixed set. In calculus, this fixed set is often the real numbers R or an interval [a, b] ⊆ R. In linear algebra, the fixed set is often Rn , Cn or an abstract vector space V (all of these terms will eventually be defined). In the discussion that follows, this ...
Contents
... Example: You have six shirts and four pairs of pants. How many distinct outfits can you create (assuming you don’t care about style)? We can think of choosing an outfit as first choosing a shirt (experience A) and then choosing a pair of pants (experience B). Overall, choosing an outfit is the exper ...
... Example: You have six shirts and four pairs of pants. How many distinct outfits can you create (assuming you don’t care about style)? We can think of choosing an outfit as first choosing a shirt (experience A) and then choosing a pair of pants (experience B). Overall, choosing an outfit is the exper ...
CS311H: Discrete Mathematics Cardinality of Infinite Sets and
... Cardinality of Infinite Sets and Introduction to Number Theory ...
... Cardinality of Infinite Sets and Introduction to Number Theory ...
CHAPTER 1 Sets - people.vcu.edu
... Definition 1.1 An ordered pair is a list ( x, y) of two things x and y, enclosed in parentheses and separated by a comma. For example, (2, 4) is an ordered pair, as is (4, 2). These ordered pairs are different because even though they have the same things in them, the order is different. We write (2 ...
... Definition 1.1 An ordered pair is a list ( x, y) of two things x and y, enclosed in parentheses and separated by a comma. For example, (2, 4) is an ordered pair, as is (4, 2). These ordered pairs are different because even though they have the same things in them, the order is different. We write (2 ...
Section 1.1 Introduction to Sets Set: A set is a collection of objects
... Thus set A contains numbers without decimals between 2 and 5 and I need to include the 2 and the 5. Answer: A = {2,3,4,5} (I wrote the A to the left of an equal sign as it is the name of this set) The curly braces in this definition are called set braces, and they are common to use when listing the ...
... Thus set A contains numbers without decimals between 2 and 5 and I need to include the 2 and the 5. Answer: A = {2,3,4,5} (I wrote the A to the left of an equal sign as it is the name of this set) The curly braces in this definition are called set braces, and they are common to use when listing the ...
section 1.1
... Thus set A contains numbers without decimals between 2 and 5 and I need to include the 2 and the 5. Answer: A = {2,3,4,5} (I wrote the A to the left of an equal sign as it is the name of this set) The curly braces in this definition are called set braces, and they are common to use when listing the ...
... Thus set A contains numbers without decimals between 2 and 5 and I need to include the 2 and the 5. Answer: A = {2,3,4,5} (I wrote the A to the left of an equal sign as it is the name of this set) The curly braces in this definition are called set braces, and they are common to use when listing the ...