Is one out of infinity different from zero?

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Discussion Overview

The discussion revolves around the concept of probability in the context of an infinite roulette wheel, specifically questioning whether the probability of one out of infinity is different from zero. Participants explore the implications of treating infinity as a number and the philosophical and mathematical nuances surrounding infinite probabilities.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions if one out of infinity is different from zero, expressing confusion about the nature of infinitely small quantities versus nothingness.
  • Another participant asserts that infinity is not a number and that expressions like 1/infinity are undefined, emphasizing the need for precise definitions in mathematics.
  • Some participants mention that treating infinity like a number can lead to ambiguous or nonsensical results, suggesting careful consideration is necessary when working with infinity.
  • It is noted that for continuous random variables with an uncountably infinite range, the probability of any particular value is zero, but this does not imply that infinity can be treated as a number.
  • Discussions arise about the concepts of actual versus potential infinity, with some participants finding these distinctions useful for understanding the limitations of treating infinity as a number.
  • One participant argues that a hypothetical roulette wheel with an infinite number of spaces is impractical, suggesting that at some point, the spaces would be smaller than fundamental physical limits, rendering the scenario nonsensical.

Areas of Agreement / Disagreement

Participants express a range of views on the nature of infinity and its implications for probability, with no consensus reached on whether one out of infinity is different from zero. The discussion remains unresolved, with multiple competing perspectives on the treatment of infinity in mathematics.

Contextual Notes

Limitations include the undefined nature of expressions involving infinity, the lack of uniform probability distributions over infinite sets, and the philosophical implications of actual versus potential infinities. These factors contribute to the complexity of the discussion.

  • #31
Why not just use a RNG on the interval?
 
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  • #32
WWGD said:
Why not just use a RNG on the interval?
A RNG can't generate a random number out of an infinite set. Nor, if you are talking about the uncountable interval (0, 1), can it generate infinite decimals. A RNG can only randomly choose an element from a finite set.
 
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