pls help....?

Question

pls explain set (in Algebra)....
all about sets....
symbols used....

pls help me....
we have a quiz tomorrow....

Answer 1

A set is simply a collection of things. It can be a collection of numbers, words, letters, food items, computer games, music . . . anything. The items don't even have to have anything in common (except that they are in the same set).

You can have a set of number that has 1, 2, 6, 7, 14, 28, and 91, or you can have a set that has 1, a printer, a small dog, a bread machine, and a TV. The possibilities are endless.

If you do have a set of the numbers 1, 2, 6, 7, 14, 28, and 91, it makes no since or write that whole sentence every time you want to write the set down. So mathematicians created set notation. In set notation that set would look like:
{1, 2, 6, 7, 14, 28, 91} it's just two curly brackets and the elements separated by commas.

Now, let's say that we want to talk about the set of all solutions to the equation sin(x)=0. We could write {. . . , -3π, -2π, π, 0, π, 2π, 3π, . . } and people would understand what all the numbers are, but let's say that we consider the set {1, 1, 4, 13, 43, . . .} it is a little ambiguous. What are the next numbers? To let people know how to find all the numbers, you can use another form of set notation. This would be:
{f(i); f(0)=1, f(1)=1, and f(i)=f(i-2)+3f(i-1)}
(the ; can be read as "where" or "with")
What this states is that the set is all of the values f(i) where f(0)=1, f(1)=1 and f(i) is defined by f(i-2)+3f(i-1).

Another example:

{2n; n is an integer}=( . . .,-6, -4, -2, 0, 2, 4, 6, . . .}

First of all, there are ways of saying "where n is an integer" in mathematics. First we define all of the integers {. . .-3, -2, -1, 0, 1, 2, 3 . . .} as Z. This is a common math notation and comes from the German word Zahl (or number). Now that we have all the integers defined a Z, we can talk about a number in the set. to say that a number x is an integer, we can use the math notation "x ε Z" which (in barbaric terms) could be read "x in Z."

Using this, we can write {2n; n is an integer}={2n; x ε Z}

Now let's say that we have two sets {a, b, c} and {c, d, e}. We can talk about the "union" of these sets or the "intersection."
The union of two sets is basically the "putting together" of them. So the union of {a, b, c} and {c, d, e} is {a, b, c, d, e}. Notice how the two sets 3 elements but the union doesn't have 2•3=6, but only 5. This is because c is in both, so you don't add it to the first set. The notation for this is {a, b, c}∪{c, d, e}={a, b, c, d, e}
The intersection is the set of elements that are in both. In this case it would be only {c} (we can have a set of one element, we can also have a set of zero elements {}, this set has nothing it it and is called the Null set and denoted by Ø). The notation for the intersection is {a, b, c}∩{c, d, e}={c}.

I'm sure that by now you have heard enough, but I'm not finished yet (you of course don't have to continue if you don't want to).

We can take two sets, and "put them together" in a strange way called the "direct product." What you do, is use one set for the first entry of an element, and the second set for the second number. This is defined by (using two sets A and B) A x B={(a,b); a ε A and b ε B}. For an example let A={1, 2}, and B={x, y}. Then the set A x B={(1,x), (1,y), (2,x), (2,y)}. You may notice that the number in elements in A x B (denoted by |A x B|) is equal to the number of elements in A (|A|) multiplied by the number of elements in B (|B|), or |A x B|=|A|•|B|.

I imagine that that should be enough. If you have any questions, just message me.

Answer 2

the symbols used are letters or numbers...therefore,sets are usually numbers

Answer 3

hope this helps
http://en.wikipedia.org/wiki/Set