BuffettIs 1 divided by 0 undefined or infinity?

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Discussion Overview

The discussion revolves around the mathematical question of whether 1 divided by 0 is considered undefined or infinite. Participants explore various perspectives on this topic, touching on theoretical implications, limits, and definitions within different mathematical contexts.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that dividing by zero is undefined, while others suggest that limits can provide different interpretations, such as approaching infinity.
  • One participant presents the limits: lim(x->0)(1/x) = undefined, lim(x->0+)(1/x) = infinity, and lim(x->0-)(1/x) = -infinity, indicating that the outcome depends on the context of the limit.
  • Another participant emphasizes that division by zero can be viewed as indefinite rather than undefined, proposing that there are problem-dependent methods to address the issue.
  • Several participants discuss the implications of definitions and properties of division, particularly in relation to the real number system and algebraic structures.
  • One participant shares a "proof" that illustrates the contradictions arising from dividing by zero, highlighting the mathematical inconsistencies involved.
  • There are references to historical perspectives on zero and its implications in mathematical operations, with some participants cautioning against oversimplified interpretations.
  • Some contributions question the relevance of certain definitions and challenge the idea that 1/0 cannot be defined in all mathematical contexts.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether 1 divided by 0 is undefined or infinite. Multiple competing views remain, with ongoing debate about definitions and interpretations in various mathematical frameworks.

Contextual Notes

Participants express differing assumptions about the definitions of division and the properties of numbers, particularly in relation to the real number system and other algebraic structures. The discussion reflects a range of interpretations and unresolved mathematical steps.

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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