benjiboo wrote:|y|<=1 (y less than or equal to 1), what does this mean?
Does it mean that y can only be 0,1,-1, or does it mean Y could be anything
Thinking about this one is confusing me, because cant it be:
|y|<=1 =
-----
y <=1
y=>-1
So y could be anything?
Here's one way to look at it:
In general, the statement: |x-k| can be thought of as the distance between x and k on the number line.
Example: |1-8| = 7 because, on the number line, the distance between 1 and 8 is 7.
Similarly, |(-3) - 2| = 5 because, on the number line, the distance between -3 and 2 is 5.
Different example: If we're told that |x-5| = 2, then we know that, on the number line, the distance between x and 5 is 2. So, x can equal either 7 or 3, since 7 and 3 are both 2 units away from 5 on the number line.
Now, the question at hand: |y|
< 1
We can rewrite this as: |y - 0|
< 1
This tells us that, on the number line, between y and 0 is less than or equal to 1.
So, which numbers are such that their distance from 0 is less than or equal to 1?
Well, all numbers between (and including) -1 and 1 are such that their distance from 0 is less than or equal to 1.
So, |y|
< 1 is telling us that: -1
< y
< 1
Cheers,
Brent
Thanks
