MAT425 Real Analysis L2

Prof. Thistleton

Open Statements, Universal Quantifier (), Existential Quantifier () (continued)

• Continuity
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
• Negating a Quantified Statement

Sets

• Containment ()
  
  
  
  
  
  
  
• Equality (A = B)
  
  
  
  
  
  
  
• Union()
  
  
  
  
  
  
  
• Intersection ()
  
  
  
  
  
  
  
• Complement(C(A))

  
  

• DeMorgan's Laws

Countable and Uncountable Sets

1.

One to One Correspondence

(a)

One to One

(b)

Onto

2.

One to One Correspondence

3.

Finite and Infinite Sets

Define the natural numbers as the familiar set {1, 2, ..., i, ...}.

4.

Cardinality

5.

Countable Sets

Theorem: N is infinite.