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Why isn't there anything which works like anti modulus? That is, a function which gives negative of absolute values of the number?

Simply, if modulus function |x| is:

when x≥0 then |x|= x and when x<0 then |x|= 0

Then why can't there be a function !x! defined such that:

when x>0 then !x!= (-x) and when x≤0 then !x!= x

If there is such a function that exists and is properly defined, please tell me about it since my maths high school textbooks have absolutely nothing mentioned about it. Thanks!

Jyrki Lahtonen
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    Please don't select tags at random just because they contain related words. In math their meaning is often very technical. The tag descriptions are there for exactly this reason. Not reading them is just lazy. – Jyrki Lahtonen Mar 21 '22 at 06:44
  • @Ayush what did you attempted? –  Mar 21 '22 at 09:12
  • Alright @JyrkiLahtonen. Really sorry for the inconvenience. I did look up modulo before adding it as a tag, but apparently I confused it with modulus. Thanks a lot for the suggestion and the edit. –  Mar 21 '22 at 18:31

1 Answers1

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For such a function, place a negative sign in front of |x|.Then,it becomes -|x|. So,for any real valued x,-|x| will be negative although |x|>=0 for all real values of x including zero.

Aravindan Sai Narayanan
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  • Well, that was pretty obvious. I was curious to know why there isn't a seperately defined function for that? Like, if you have to find the difference between X and Y, you can simply write it as a sum of X and (-Y), but we also have a dedicated subtraction operation. –  Mar 21 '22 at 06:23
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    And any facts about this function will follow immediately and trivially from facts about the absolute value function, which is why no one (until now) has ever bothered mentioning it – Gerry Myerson Mar 21 '22 at 06:23
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    Alright, I think I got my answer. Thanks @GerryMyerson. –  Mar 21 '22 at 06:24