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Negative numbers are the same as positive numbers: discuss.

Discussion in 'Mathematics' started by Kez101, Nov 21, 2011.

  1. In real life, in some applied Maths, negative numbers and positives are absolutely not the same.
    Take a business.
    It makes profits (positive numbers). It pays taxes and can give it's owners money because it's successful. Bigger the profit the better.
    OR
    It makes losses (negative numbers). It may get tax refunded and it may need the owners to invest money or borrow money for it to survive. The bigger the loss, the worse it is.
    It is, in this scenario, really important the number is a positive one and no way could anyone describe negatives (losses) and positives (profits) as being the same.
     
  2. OK null, if you want to be pedantic, the group is (Z,+).
     
  3. tafkam

    tafkam Occasional commenter

    Playing devil's advocate, in some senses you could argue that this shows that the two are the same. For example, if we scale it right down, someone running a massive business that was used to profits of millions would presumably find a £1 profit as worrying as a £1 loss. The final £2 extra drop would presumably be a "drop in ocean"

     
  4. It doesn't show they are the same, but it does show that the closer they are the closer to being the same they are. So, yes, for anyone there is little difference between £1 profit or £1 loss but as you get further away from 0 the magnitude of difference is greater, say the difference between making a profit of a million or a loss of a million.
     
  5. I suppose because I don't understand what you mean when you say

    I'm probably just being thick.
     
  6. afterdark

    afterdark New commenter

    The whole point of a discussion is to highlight /find misconceptions and establish what is meant by fundamental ideas.
    +9 and -9 are both 9 steps away from zero and the sign distinguishes the direction. This should easily arise in a class discussion. Perhaps with an arrow or 2 drawn to prompt them if absolutely needed. [​IMG]
    This was, IMHO, the kind of thing that tafkam was getting at.
    It can be fruitful to ask students if they are now clear on an idea. I believe the new "buzz phrase" for this is "AfL".

     

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