{x | x is a
natural number less than 4}
There are two parts to this:
Putting these two ideas together we get
{1, 2, 3}
{x | x is
a whole number between 100 and 105}
There are two parts to this:
Putting these two ideas together we get
{101, 102, 103, 104}
{x | x is an
odd whole number greater than 5}
There are three parts to this:
Putting these two ideas together we get
{7, 9, 11, 13 ...}
{-3, -3/2, 0, .25, 1}
Note that we have two non-integer numbers to graph. The -3/2 will go halfway between -2 and -1. The .25 will go between 0 and 1, a little closer to 0 than 1.
Natural numbers
The numbers in the given set that are also natural numbers are
{2, }.
Note that simplifies to be 3 which is a natural number.
Whole numbers
The numbers in the given set that are also whole numbers are
{0, 2, }.
Integers
The numbers in the given set that are also integers are
{0, 2, }.
Rational numbers
The numbers in the given set that are also rational numbers are
{-1.5, 0, 2, }.
Irrational numbers
The number in the given set that is also an irrational number is
{}.
Real numbers
The numbers in the given set that are also real numbers are
{-1.5, 0, 2, ,}.
0 ? {x | x is a rational number}
Since 0 can be written as 0/1 (one integer over another), it is a part of the list of rational numbers. So it would be true to say
0 {x | x is a rational number}.
10 ? { 2, 4, 6, 8, ...}
The ellipsis in the set indicate that the pattern of numbers (even natural numbers) would continue, which means 10 would be included in this list. So it would be true to say
10 {2, 4, 6, 8, ...}.
? {x | x is an irrational number}
Since simplifies to be 2, which is a rational number, it can not be an irrational number. Therefore,
{x | x is an irrational number}.
Since EVERY element of Q (rational numbers) is also in R (Real numbers), this statement is TRUE.
Since EVERY element of R (Real numbers) is not also in Z (Integers), this statement is FALSE.
|10|
When looking for the absolute value of 10, we are looking for the number of units (or distance) 10 is from 0 on the number line.
I came up with 10, how about you?
- |-10|
This problem has a little twist to it. Let's talk it through. First of all, if we just concentrate on |-10| we would get 10. Then, note that there is a negative on the OUTSIDE of the absolute value. That means we are going to negate what we get for the absolute value.
Putting that together we get -10 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.
½
The opposite of 1/2 is -1/2, since both of these numbers have the same absolute value but are on opposite sides of the origin on the number line.
-20
The opposite of -20 is 20, since both of these numbers have the same absolute value but are on opposite sides of the origin on the number line.
Last revised on June 10, 2011 by Kim Seward.
All contents copyright (C) 2002 - 2011, WTAMU and Kim Seward.
All rights reserved.