Hi, I'm taking probability class. We only use materials that is provided by our instructure and we dont use book. It's kind of hard for me to understand what is the concept because there is no example is given that I can related to to concept.
I'm having trouble with
1. Provide, if possible, an example of an object collection that is infinite.
2. What is meant by the statement that an object collection M is not infinite?
Now, before helping me, here is what is given.
I) The statement that P is an ordered object pair means there is an object a, called the first object, and there is an object b, called the second object. We shall denote such an ordered object pair by (a,b). We may call a the first element of the ordered pair and b the second of the ordered pair.
So far so good. Completely making sense to me.
II) Suppose each of A and B is a set. The statement that f is a function from A into B means:
a) f is an ordered element pair collection;
b) only (a,b) belongs to f when a is in A and b is in B;
c) No two such ordered pairs have the same first element.
This is where it starts to not make sense to me...there is no example that shows why that is true and I can't exactly prove it even though this is a rule.
The set to which only x belongs when x is the first element of an ordered pair belonging to f is called the initial set, or domain, of f and is denoted by D sub f.
The set to which only y belongs when y is the second element of an ordered pair in f is called the final set, or range, of f and is denoted by R sub f.
If (u,v) is an ordered pair in f then we may denote v by f sub u or f(u) and the pair (u,v) by (u, f sub u) or (u, f(u)).
If D sub f is a collection of one or more sets, that is, if each member of D sub f is a set, then f is said to be a set function.
Finally, if every element of set B is in R sub f, then f is said to be from A onto B.
The statement that an object set S is infinite means that if n is any positive integer greater than 1, then S has (at least) n objects.
At this point, I can't even make sense of any of this without understanding what the 3 points mean earlier in this message. Can anyone help me?