Those objects are generally called elements of the set. The symbol means 'is an element of. 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.
It is also written between two set brackets. 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. 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. 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. Be careful. 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.
The natural numbers and the whole numbers are both subsets of integers. Be very careful. Remember that a whole number can be written as one integer over another integer.
The integer in the denominator is 1 in that case. The natural numbers, whole numbers, and integers are all subsets of rational numbers. It is a non-repeating, non-terminating decimal. One big example of irrational numbers is roots of numbers that are not perfect roots - for example or.
Similarly, 5 is not a perfect cube. It's answer is also a non-terminating, non-repeating decimal. Another famous irrational number is pi. Even though it is more commonly known as 3. Actually it is 3. It would keep going and going and going without any real repetition or pattern. In other words, it would be a non terminating, non repeating decimal, which again, can not be written as a rational number, 1 integer over another integer.
That would include natural numbers, whole numbers and integers. Example 4: Graph the set on a number line. In this problem, we have a -. Since it is halfway between these two numbers, I would place the dot halfway between. The other numbers are integers that are already marked clearly on the graph. Natural numbers? Note that simplifies to be 5, which is a natural number. Whole numbers? Rational numbers? Irrational numbers? They are non-repeating, non-terminating decimals.
Real numbers? Example 6: Place a or to make the statement true. Example 7: Place a or to make the statement true. Example 8: Place a or to make the statement true.
Example 9: Place a or to make the statement true. Example Determine if the statement is true or false? In fact, there are no elements in N that are in I. Absolute Value Most people know that when you take the absolute value of ANY number other than 0 the answer is positive. But, do you know WHY?
Well, let me tell you why! Distance is always going to be positive unless it is 0 whether the number you are taking the absolute value of is positive or negative. The following are illustrations of what absolute value means using the numbers 3 and Example Find the absolute value. I came up with 7, how about you? Example Find the absolute value. Let's talk it through. First of all, if we just concentrate on -2 , we would get 2.
That means we are going to take the opposite of what we get for the absolute value. Putting that together we get -2 for our answer. Note that the absolute value part of the problem was still positive.
We just had a negative on the outside of it that made the final answer negative. Opposites Opposites are two numbers that are on opposite sides of the origin 0 on the number line, but have the same absolute value. In other words, opposites are the same distance away from the origin, but in opposite directions.
The opposite of x is the number - x. Keep in mind that the opposite of 0 is 0. When you see a negative sign in front of an expression, you can think of it as taking the opposite of it. For example, if you had - -2 , you can think of it as the opposite of Example Write the opposite of 1. The opposite of 1. Example Write the opposite of The opposite of -3 is 3 , since both of these numbers have the same absolute value but are on opposite sides of the origin on the number line.
Practice Problems. At the link you will find the answer as well as any steps that went into finding that answer. Practice Problems 1a - 1c: List the elements of each set. Practice Problem 2a: Graph the set on a number line. This shows it isn't a perfect square which also proves that the square root of is an irrational number.
As is a prime number hence it cannot simplified any further. Let us now try finding the square root of by the long division method. On continuing further we can estimate the value of square root of to as many places as required.
Example 2 : James wants to buy a new rug for his room. In the store, he finds a square rug that has an area of sq feet. Help James find the length of each side of the rug?
The area of rug is square feet. That means the length of each side of the rug is the square root of its area. Hence, the length of each side of the rug is We can simplify it by pulling out the number which is multiplied to itself. What Is the Square Root of ?
Is Square Root of Rational or Irrational?
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