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B What is math without 0 like?

  1. Nov 18, 2015 #1
    It's something I've been thinking about recently, would math be simpler or way more complicated without 0?

    1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18,19,21...

    I've been trying to do some simple equations without 0, and with small numbers the results are usually the same. But would getting rid of 0 solve any problems, for example dividing 0 by 0. I'm not sure how much this has been thought about before and if there has been any reasoning why this would be a terrible idea so I'd like your guy's opinions on the matter.
     
  2. jcsd
  3. Nov 18, 2015 #2

    jedishrfu

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  4. Nov 18, 2015 #3

    fresh_42

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    "People first could handle their crop through counting and adding. But as soon as they started borrowing crop, they had to turn to negative numbers to get theirs accounts balanced. Necessary for it was by the way the discovery of zero, which wasn't easy at the times. Why should one count nothing? It took a while."

    Eliminating the 0 is nothing else than counting. It has nothing to do with calculation, computing or any modern science any more.
    You could ask as well how it would be if we only can count to 5 since we have just 5 fingers. But even the Neanderthals could count further ...
     
  5. Nov 18, 2015 #4

    micromass

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    OK, but this is actually irrelevant. You can have 0 as a placeholder and still not accept the existence of 0 by itself. In fact, that is what most ancient civilizations actually did.
     
  6. Nov 18, 2015 #5
    The Romans had no zero.
    (Although I expect some of the soldiers who didn't get paid after losing a battle were well able to grasp the concept)
     
  7. Nov 19, 2015 #6

    Svein

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    There are at least answers to this:
     
  8. Nov 19, 2015 #7

    micromass

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  9. Nov 19, 2015 #8

    pwsnafu

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    We don't know of any Roman numeral for zero before 725 (which is first use of N for zero we know of). We do know that the word nulla was used for the concept.
     
  10. Nov 19, 2015 #9
    You had as many apples as you had before you went apple picking. Why go through all the trouble of recording no change?
     
  11. Nov 19, 2015 #10

    PeroK

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    You'd lose associativity:

    ##(2 + 1) - 1 = 3 - 1 = 2##
    but
    ##2 + (1 - 1)## would de undefined.

    We already have to take care that a denominator is not 0, and this would extend to everything. If you have ##x-y## anywhere, you'd have to exclude the case ##x = y##.

    ##cos(\pi/2)## would be undefined. But, then ##tan(\pi/2)## is not defined and we manage that.

    Losing the concept of zeroes of a function would be a major loss, I would say.

    I'd prefer to exclude a number like 673, since that doesn't turn up very often. Missing out 673 would be much easier to deal with.
     
  12. Nov 19, 2015 #11

    FactChecker

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    If I had $5 and owed someone $5, what would my net worth be? How can simple calculations be done without 0? In abstract algebra, the simplest thing above a "set" is the "group". A group requires an "identity" element, which, when added to another number, causes no change. That is 0. Without that it is not possible to do even the simplest math.
     
  13. Nov 19, 2015 #12
    You could use a placeholder or simply not write anything at all. You can do even the simplest of math without 0.
     
  14. Nov 19, 2015 #13

    PeroK

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    You can do a lot of maths without 673. Even more than you can do without 0.
     
  15. Nov 19, 2015 #14

    Svein

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    Then how would you detect the difference between "haven't written anything" and zero?
     
  16. Nov 19, 2015 #15
    Okay, sure but that wasn't the topic. Although now I'm curious why 673 is so useless. Does it just not appear much in any equations?
     
  17. Nov 19, 2015 #16

    PeroK

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    Have you ever used the number 673?
     
  18. Nov 19, 2015 #17
    You could do something like

    net worth:

    I know using a placeholder would be better, but wouldn't having no 0 in equations save much room on the whiteboard. We can still define variables with a placeholder or just the word nothing/empty or something more technical if you prefer.
     
  19. Nov 19, 2015 #18
    Good point.
     
  20. Nov 19, 2015 #19

    Svein

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    Yes, of course, we mathematicians are a lazy lot. It is much easier to write "0" than "nothing".
     
  21. Nov 19, 2015 #20
    I understand. I'm not talking about when defining the value of something with 0. I'm talking about larger numbers and simply not showing anything if it has no value. We could even just use 0 as a placeholder but get rid of 10s, 20s etc.
     
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