|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?
Please provide explanation with your answer Thanks
|y|<=1 (y less than or equal to 1), what does this mean?
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|y|<=1 think about y as the distance on the number line between 0 and a value, number (discreet or continuous) here discreet and 1, that's exactly what the sign of modulus tells us the distance on the number line within the brackets | |
now it also tells us that the distance is equal or less than 1. This means that we can have our y within the range of -1 _____0______1 where -1 and 1 are also included.
we are having the continuous value's range as we have no restriction set, such as y must be integer
now it also tells us that the distance is equal or less than 1. This means that we can have our y within the range of -1 _____0______1 where -1 and 1 are also included.
we are having the continuous value's range as we have no restriction set, such as y must be integer
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?
Please provide explanation with your answer Thanks
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Here we go, as per the gist of absolute value, i.e. module of number or |y|<=1 means following:
y<=1 and y>=-1 and this means that y belongs to the segment [-1;1], hence, y could be one of infinite numbers from the segment set forth above. If, y is an integer so it could be either -1, 0 or 1.
In general |x| means x if x>=0 and -x if x<0
Please, correct me if I went awry
y<=1 and y>=-1 and this means that y belongs to the segment [-1;1], hence, y could be one of infinite numbers from the segment set forth above. If, y is an integer so it could be either -1, 0 or 1.
In general |x| means x if x>=0 and -x if x<0
Please, correct me if I went awry
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Here's one way to look at it: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?
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