# Thread: Sets and Elements

1. ## Sets and Elements

Q: Show that the set
A = {±1 ± 2 ± 3 ± ... ± 2006}
contains an even number of elements.

I have no idea where to start or how to do this

2. Originally Posted by unstopabl3
Q: Show that the set
A = {±1 ± 2 ± 3 ± ... ± 2006}
contains an even number of elements.
If one adds two even numbers does one get an even number?
Is the number of elements in $\displaystyle \{1,2,3,\cdots,2006\}$ even?

3. it doesn't matter whether the number of elements in (1...2006) is even (the answer is yes, because 2006 is an even number). The point is that you have the negative numbers as well. So the number of elements in the set is double the number in (1....2006), so it must be even.

Step by step
that is just the positive integers, and the negative integers (up to 2006).

ie, every positive integer and its negative partner

ie, every element can be paired with another one

so there must be an even number

Edit Posted while plato was typing and not intended to disrespect his answer

4. Thanks for the replies, but how would I show this in mathematical terms or a simple statement?

5. Originally Posted by unstopabl3
Thanks for the replies, but how would I show this in mathematical terms or a simple statement?
What is the answer?

6. Well "Yes" the number of elements are even ...

7. Originally Posted by unstopabl3
Well "Yes" the number of elements are even ...
That is not what I meant. How many elements are there in the set?

8. 2006 x 2 = 4012 , which is an even number ???

9. Correct! Now you have done the question.

10. Thanks, both of you!