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If a/x*x = a then if x =0 a/0*0 = a

  1. Apr 20, 2005 #1
    if

    a/x*x = a

    then if x =0

    a/0*0 = a

    but they say that:

    n *0 = 0

    and when n =a/0

    so that

    a/0*0 = 0

    instead of a
     
  2. jcsd
  3. Apr 20, 2005 #2
    a/0 does not = 0

    anything/0 is undefined
     
  4. Apr 20, 2005 #3
    do you know that long ago when some one asked what 5-6 was, he was told undefined(ok not exactly that, but something that meant impossible)

    sooner to present day, some was told that (-4)^.5 (that is square root of -4 without using square root sign) was impossible, untill someone thought outside the box and cam up with imaginary numbers.

    time to do that again
     
  5. Apr 20, 2005 #4
    5*0 = 4*0

    If you can divide by zero, then the zeros cancel and 5 = 4 and you end up with a number system with only 1 element. Its not so much impossible to come up with a system that allows you to divide by zero, its that it would be limiting rather that useful..
     
  6. Apr 20, 2005 #5

    Hurkyl

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    And they were right.

    And they were right.


    It's not a matter of "thinking outside the box" -- it's a matter of definition. Long ago, people used a number system that consisted only of positive numbers. Thus, it is correct that 5-6 was undefined. And it's still undefined in that number system. The fact we invented negative numbers doesn't change that fact.

    Similarly for your next example.


    The problem with wanting to invent division by zero is this:

    0 = 0*x - 0*x = (0 + 0)*x - 0*x = (0*x + 0*x) - 0*x = 0*x + (0*x - 0*X) = 0*x + 0 = 0*x

    Each of the steps in this equation is something that is extremely desirable for a number system to have. Here, I've used:
    Subtracting something from itself yields zero.
    Adding zero to something leaves it unchanged.
    Multiplication distributes over addition
    Addition is associative.

    Thus, anything that has these nice properties also has the property that 0*x = 0 for all x.

    Thus, if we wanted to define division by zero, we must have:

    0*x = 0 = 0*y
    Therefore x = y. (Dividing by zero)

    In other words, it would require every number to be equal to every other number. That's not a very interesting number system now, is it? :biggrin:

    In order to have a useful division by zero, one has to give up at least one of the properties that makes a number system useful.
     
  7. Apr 21, 2005 #6
    so hurky you mean that the number system where every number to be equal to every other number isn't interesting.

    and by the way i'm confuse wether 1/0 = undefined or infinity

    if i asked u that wether

    1/0 < 2/0

    if yes then 1/0 suppose to be a form of constant
     
  8. Apr 21, 2005 #7
    It is just undefined(not infinity).

    Let us say, 1/0 = infinity. As infinity still holds some mathematical value 0*infinity = 0, thus 1 = 0.

    When a teacher was explaining his elementary school students about dividing a number with same number and always getting the value 1, he took an example of distributing 5 apples among 5 students, 4 apples among 4 students etc.

    A boy stood up and asked that if there were no apples and they were distributed to nobody, still everybody would get 1 each?

    The boy asking about division by zero was the great Srinivasa Ramanujam and he was 8 year old that time.
     
  9. Apr 21, 2005 #8
    I am sorry. On a second thought, my explanation seems to be wrong for, 1/infinity = 0 and so if infinity*0 = 0 then 1 = 0.

    You just consider 1/0 is undefinied.
     
  10. Apr 23, 2005 #9
    so if we have a curve where y= 1/x and at a point where x=0, was taught that y = infinity instead of undefined. infinity point on cartesian plane is somewhere imaginary. while undefine should be nowhere or does not exist.
     
  11. Apr 23, 2005 #10
    y = infinity means y is undefined.
     
  12. Apr 23, 2005 #11
    Does someone know which are the different types of undefinitions in math?

    and esclusively, what is zero times infinite?
     
    Last edited: Apr 23, 2005
  13. Apr 25, 2005 #12
    when x approaches 0, y approaches +infinity or -infinity depending on direction... that's one of the reasons 1/0 is undefined.

    there is no point at x= 0, it is untrue that "there is an imaginary point...", it does not exist.
     
    Last edited: Apr 25, 2005
  14. Apr 25, 2005 #13
    this doesnt work becaus infinity/infinity does not equal 1, it is undefined.

    for <<<GUILLE>>>, 0*infinity = 0
     
  15. Apr 25, 2005 #14

    thanks.

    and zero/infinity?

    and infinity/zero?
     
  16. Apr 25, 2005 #15
    zero/infinity = 0 ...anything not (+,-) infinity is zero when divided by (+,-) infinity (this may actually be undefined, but its limit is 0)

    infinity/zero DNE
     
    Last edited: Apr 25, 2005
  17. Apr 25, 2005 #16
    thanks again.

    one more, what is -infinite+infinite?
     
  18. Apr 25, 2005 #17

    HallsofIvy

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    There are not "different kinds" of "undefined"s. "Undefined" means exactly that: there is no definition for that combination of symbols- it makes no sense. As far as the real numbers are concerned, any formula involving "infinity" is "undefined" because infinity itself is undefined. Asking "what is 0/infinity" is exactly the same as asking "what is 0/green beans?".
     
  19. Apr 25, 2005 #18

    T@P

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    isnt the more clear cut way of saying it like this: anything/0 is undefined over real numbers. however, when you get the limit thing, like lim 1/x as x -> 0, you get infinity bcause that is what it 'approaches'. but in general, in a pure math situation, if you come across 1/0 give up right there.

    ofcourse, in most cases the 1/0 comes up in an 'applied' or semi applied problem, like some word problem or such, and when you solve the quadratic you come up with an imaginary number. that doesnt mean your equations are 'undefined', it means that relative to your specific example, you interpert a result of 'undefined' as the dog missed the train, or whatever. same idea with 1/0, if you have say an equation for profit an thats what you get, your profit is mathematically undefined, but if you think of it relative to that case it means your profit is 'infinite'.

    so in a sense, i agree with Hurkyl, but i think that you're being a little over formal/general/precise. (I mean duh thats not quite what people mean when they write 5-6 :) )
     
  20. Apr 25, 2005 #19

    Hurkyl

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    First off, there is no infinity in the reals, so this would be an undefined statement in the reals.

    Secondly, in terms of the extended reals, it is still undefined.

    Thirdly, in terms of limit forms, 0 * infinity is an indeterminate form. (Consider, for example the limits of x * 1/x, and x * 2/x)
     
  21. Apr 26, 2005 #20
    1/0 < 2/0
    do you agree...
     
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