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04 Aug 2021, 04:55
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How |y| = –y can be translated into y ≤ 0?
04 Aug 2021, 05:29
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anurag0928
Now MOD is always non negative.
So, |y|\(\geq 0\).
This means \(-y\geq 0\).
Change the sign by multiplying by -1 => \(-1*-y\leq 0*-1………y\leq 0\)
04 Aug 2021, 06:46
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anurag0928
Absolute value can be thought of as 'distance from 0.' Distance is never negative.
So if y > 0, the distance from 0 is just... y.
Like |10| = 10, because 10 is 10 from 0.
But if y < 0, you can't say |y| = y.
|(-10)| ≠ -10, right?
|(-10)| = 10 = -(-10)
So |y| = -y if y < 0
(The difficult thing about this is that with negative numbers, the negative is 'outside' the number. -10 looks like 'two things': -1*10.
With variables we can 'bury' the negative in side the letter. 'y' doesn't look negative, but if y = -a, for some a>0, then y is negative. The negative sign is just 'part of' the y).
