Make your own calendar (month of June and July) using rational and irrational number.
Answers
Step-by-step explanation:
Above is an illustration of a number line. Zero, on the number line, is called the origin. It separates the negative numbers (located to the left of 0) from the positive numbers (located to the right of 0).
I feel sorry for 0, it does not belong to either group. It is neither a positive or a negative number.
When graphing a point on the number line, you simply color in a point that corresponds to that number on the number line as illustrated below. That is how you graph a solution on the number line.
This is how you would graph it if your solution was the number 2:
point
Sets and Elements
A set is a collection of objects.
Those objects are generally called elements of the set.
The symbol element means 'is an element of.'
So, it stands to reason that not an element represents 'is not an element of.'
Subset
We say that A is a subset of B, written A subset B, when every element of A is contained in B.
(It does not necessarily mean that every element of B is also contained in A)
Ways to Notate Sets
There are several ways to notate a set, the two most common ways are:
the roster form and
set builder notation.
Roster form just lists out the elements of a set between two set brackets. For example,
{January, June, July}
Set builder notation describes the members of the set without listing them. It is also written between two set brackets. For example,
{x | x is a month that begins with J}
When writing it in set builder notation you always do the following: start off with a left set bracket, then you put x followed by a vertical bar which is interpreted as 'such that'. Then you write out the description of the elements of the set. Finish it with a right set bracket.
So the above illustration would be read: "x, such that, x is a month that begins with J."
It is important to know set builder notation, especially in mathematics, because it allows you to group together large number of elements that belong to a certain category. The above set has only 3 elements, so it would not be difficult to write it in roster form as shown above. However, if your set has hundreds or thousands of elements, it would be hard to list them out, but easy to refer to them using set builder notation. For example, {x| x is a college student in Texas}.
Before we move on to the math aspect of sets, there is one more term we need to make sure you have a handle on.
Empty Set
Empty (or null) set is a set that contains no elements.
It is symbolized by { } OR empty set .
Be careful. It is real tempting to use them together, but {empty set} IS NOT a way to indicate empty set.
Let's move on to some special sets that pertain specifically to math.
Note that the three dots shown in the sets below are called ellipsis. It indicates that the elements in the set would continue in the same pattern. - In other words, the list would keep going and going in that direction using the pattern illustrated.