Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

Why do people not accept the fact that any number divided by zero is infinite, and is not undefined? Or am I wrong after all?

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  • Ray S
    Lv 7
    1 month ago
    Favorite Answer

          If 1/0 is defined, then 0 times 1/0 would have to be a unique number in order for our system of mathematics to be consistent. So, would you have 0*(1/0) be 0 or would you have it be 1? And, what would 0/0 be?

          Any number divided by another non-zero number can be plotted as a point on the number line whereas a number dived by zero cannot, because, infinity is not a number. Infinity is an elusive destination that can never be reached, and so, cannot be plotted.

          It is true that for n  >  0, 1/n gets larger and larger as n gets closer and closer to zero so that 1/n heads for infinity. So the limit of 1/n as n goes to zero IS defined as being infinity. But, that's not the same as saying that 1 divided by the stationary, i.e. plottable number 0 is itself a real and plottable number.

          Division by zero is undefined, because, it would generate an inconsistency in our system of mathematics that would make mathematics unreliable. And, we can't have that ... Division by zero cannot be defined for that reason.

  • 4 weeks ago

    We'll, lets see.  If there are 10 dollars on the table waiting to be divided equally among ten people in the room but the ten dollars are never divided among them then it ends up that the 10 dollars still remain. 10 ÷ 0 = 10. Take the money and run because mathemticians will tell you you have nothing and pocket the 10 themselves.

  • 4 weeks ago

    12 divided by 4, for example means take 12 things and divide them into groups of 4, and see how many groups you get (3).

    So 4 divided by zero for example means take 4 things and divide them into groups of zero things.  You can't do it since by definition a group has to have at least 1 thing in it, so division by 0 is undefined.

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  • Anonymous
    1 month ago

    A zero is nothing.... I mean nothing, zip.  And you divide 1 by zero.... and the answer is 1 or the number itself.   you learned so much but forget to use your brain.

    PS: the limit of 1/0 is infinite....

  • geezer
    Lv 7
    1 month ago

    ''Any number''

    So ..

    What is 0/0 then ?

    Infinite, undefined, 0 .. or 1 ?

    • roderick_young
      Lv 7
      4 weeks agoReport

      I believe @geezer is trying to stimulate thinking from the original poster, and knows the answers.

  • D g
    Lv 7
    1 month ago

    1/3 = 0.333333...

    3 x .333333... = 1

    The function is reversible to get the numerator

    3/infinity = 0 according to you

    0 x infinity = 0

    Anything times 0 gives 0

    It approaches but never gets to it that's why we have things like asymptotes 

  • 1 month ago

    1/x = y only if 1 = xy

    0 times ANYTHING = 0

    IF 1/0 = y, then 1 =0

    You've created a paradox, therefore you cannot divide by 0 and have a known value.

    Therefore, you may not divide by 0, it's undefined.

  • 1 month ago

    The limit as x approaches zero of 1/x is infinity. But 1/0 is undefined. This is a technical point but it is important.

    Division by zero is never allowed. There would be many contradictions produced if we allowed it and called it infinity.

    • Jeffrey K
      Lv 6
      4 weeks agoReport

      Excellent point Lisa! You are right. The limit as x approaches zero from the negative (left) side is negative infinity. The two limits don't match, so this limit does not exist. 

  • 1 month ago

    i dont think youre wrong

    • Fran6 days agoReport

      2 wrongs don't make a wright but 2 wright's made an airplane.

  • david
    Lv 7
    1 month ago

    People do not accept that division by 0 has an answer of infinity because it is not true.  ===  Mathematically division is defined as the opposite operation of multiplication  ....  2X3 = 6, so  6 / 2  =  3

      so  1 X 0 = 0  ... so  0/0 =  1??  

     and  3 X 0 = 0  ...  0/0  =  3 ???  so division by 0 would not be defined as infinite, but as any number that you want as an answer  ====  Math does NOT like that multiple answer to the same or similar problems and therefore some old dead guys looking at this problem years ago said that to avoid the confusion we will have to agree that division by 0 is undefined.

    ==============================

    Forget Math definitions .. use common sense

       12 / 1 = 12

        12 / 2 = 6

       12 / 3 = 4  .... why??

     in grade school you were told that division  is making groups the same size

        If I have 12 apples and I divide the evenly by 3 friends how many apples does each friend get?

      (4A) + (4A) + (4A)  = 12A

      so you make 3 groups of 4A each .. each person gets 4 apples.  12 / 3  = 4

       ...   so I have 1 apple and I want to give equal amounts to 0 friends  how many apples does each friend get?

       1 / 0  =  infinity ???  where did the infinity number of apples come from?  you only had 1 to start with.

    • david
      Lv 7
      4 weeks agoReport

      Jeffery K ===  sin X / X is NOT equal to 1  ==== that is a limiting value.  === The limit as x APPROACHES 0 (but is never allowed to equal 0) is 1 

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