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A zero multiplication paradox

  1. Dec 18, 2014 #1
    If Anna has 0 coins and Bertus has 0 coins aswell. Can you say that Anna has twice as much coins as Bertus? Because 2*0=0. But couldn`t you also say that Anna has four times more coins than Bertus, but simultaneously Bertus has 5 times more coins than Anna? Making it a paradox?
  2. jcsd
  3. Dec 18, 2014 #2


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    This is not a paradox. Because for x=0, x=1x=2x=3x=4x=..., so you're just giving different names to the relationship between the two number of coins.
  4. Dec 18, 2014 #3


    Staff: Mentor

    I agree with @Shyan that this isn't a paradox. The product of any finite number and zero is zero.
  5. Dec 18, 2014 #4
    I agree mathimatically, but in a social concept where Anna says she has twice as much coins than Bertus, while Bertus can say at the same time he has 5 times more as coins than Anna.
  6. Dec 18, 2014 #5


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    No paradox. You want to solve the equation A=xB, where x is the multiplier of how many more coins Anna has than Bertus. Now since A = B, then x = 1, or A/B = 1.

    0/0 , which is indeterminate in general, in this specific problem is a specific number, namely, 0/0 is 1. Anna has the same number of non-existing coins as Bertus, none, no more, no less.

  7. Dec 18, 2014 #6


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    Its not a paradox even in that sense. You can test it. Tomorrow, go out and explain it to the first person you see and ask whether s\he thinks this is a paradox. Chances are very high that s\he tells you this is not a paradox and explains the reason very quickly.
  8. Dec 18, 2014 #7
    If it`sa paradox ir not is not really my point, sorry english isn`t my native language. I mean can Anna say that she has twice as more coins than Bertus and Bertus can say at the same time that he has 5 tikes as much coins than Anna?
  9. Dec 18, 2014 #8


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    Yes, because 0=0, no matter how those zeroes look like!
  10. Dec 21, 2014 #9
    Yes, it's a language paradox or a language spin, a better word. For example if you and I run a race and you beat me by a mile, I can say that I finished second while you came in next to last! It's expressing the truth in such a way as to give the opposite impression. That's what politicians call spin.
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