BuffettIs 1 divided by 0 undefined or infinity?

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SUMMARY

The forum discussion centers on the mathematical concept of dividing by zero, specifically whether 1 divided by 0 is undefined or infinite. Participants assert that in the standard real number system, division by zero is strictly undefined, while limits approaching zero can yield infinite results. The conversation highlights the importance of defining terms and understanding the properties of division, particularly in relation to zero and infinity. Ultimately, the consensus is that 1/0 does not exist within the framework of real numbers.

PREREQUISITES
  • Understanding of basic arithmetic operations, particularly division.
  • Familiarity with limits in calculus, specifically the concept of limits approaching zero.
  • Knowledge of real number properties and definitions in mathematics.
  • Awareness of mathematical terminology related to infinity and undefined expressions.
NEXT STEPS
  • Study the concept of limits in calculus, focusing on limits involving division by zero.
  • Explore the properties of real numbers and the implications of division by zero in various mathematical systems.
  • Investigate the extended complex plane and how it handles division by zero.
  • Review mathematical proofs that illustrate the contradictions arising from division by zero.
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Mathematics students, educators, and anyone interested in understanding the complexities of division by zero and its implications in various mathematical contexts.

1 divided by zero=?

  • Undefined

    Votes: 8 61.5%
  • Infinity

    Votes: 2 15.4%
  • Other(explain):

    Votes: 3 23.1%

  • Total voters
    13
  • Poll closed .
  • #31
master_coda said:
Your definition of division is not the same as the definition of division on the real numbers.

i guess you're implying the irrational numbers. i was not willing to expand the algorithm for non-integer results. i have never given any irrational number input. if you mean the non-integer results.. well, here it goes:

let A and B two reel numbers. subtract B from A until A is bigger or equal to zero, and add 1 to the division at each step. after this process, if A is negative, undo the one step. multiply A with 10 (or what ever the step is) and add 10^{-1} to the result after each subraction. repeat these steps until A=0, and decrement the power of 10 (to generalize, base) by 1.

however, i'd like to point that the original question is integer-wise, and this definition was uncessary.
 
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  • #32
fdarkangel said:
i guess you're implying the irrational numbers. i was not willing to expand the algorithm for non-integer results. i have never given any irrational number input. if you mean the non-integer results.. well, here it goes:

let A and B two reel numbers. subtract B from A until A is bigger or equal to zero, and add 1 to the division at each step. after this process, if A is negative, undo the one step. multiply A with 10 (or what ever the step is) and add 10^{-1} to the result after each subraction. repeat these steps until A=0, and decrement the power of 10 (to generalize, base) by 1.

however, i'd like to point that the original question is integer-wise, and this definition was uncessary.

But you attempted to extend the algorithm to try and divide by zero. Once you do that, the algorithm is no longer giving the same results as real number division.
 
  • #33
it does, for integer results.
i expanded the algorithm to generalize. basics of both division methods are same. the initial explanations i made about 1/0 and 0/0 are still correct. please don't be so pedantic, the interger-only algorithm is consistent and sufficient enough to explain 1/0.
 
  • #34
fdarkangel,

Again, you are wrong. Master_coda is correct. Your algorithm is, basically, junk.

Either way, this thread is just a rehash of many other similar threads here. We don't need another thread with the same arguments from the same people.

Thread closed.

- Warren
 

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