MATH 311-02
1
Notes
Introduction to Higher Math
Introduction
Go over the syllabus, noting in particular the assessment dates and the need for class participation.
2
The Language of Math
Chapter 0 gets somewhat ahead of itself on background, but gives some
MATH 311-02
1
Notes
Introduction to Higher Math
Unions and Intersections
There are two particularly elementary binary operations on sets: union and intersection.
The union of two sets A and B , denoted A B , is the set consisting of everything that is a
m
MATH 311-02
1
Notes
Introduction to Higher Math
Indexed unions, part 2
Indices can also be drawn from arbitrary sets, so we might refer to the indexed collection cfw_Ax xR ,
given by, for instance, Ax = cfw_y R : y isanintegermultipleof x, so for instance
MATH 311-02
Notes
Introduction to Higher Math
1
Logic: Statements concluded
We ordinarily give statements names, usually P or Q or subscripted versions thereof. We might let P be "2+2-5", which is a false statement, or let Q be "x is a rational number", w
MATH 311-02
Notes
Introduction to Higher Math
1
Logic: Necessity and sufficiency
Hearken back to the "abstention from pork" example: "if x is a vegetarian, then x abstains from pork". We could state this in terms of the concept of necessity, as such: Abst
MATH 311-02
1
Notes
Introduction to Higher Math
Logic: Quantiers
We often wish to state that a statement is globally true. For instance, we might say: for all real x,
x2 is positive. This is what is referred to as a universally quantied statement. Univers