Can the probability of an event ever be exactly zero?

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The discussion centers on the probability of an event occurring at an exact moment in a continuous time framework. It is argued that while the probability of a specific event happening at an exact time, like 1 minute, is mathematically zero due to infinite possible outcomes, this does not imply that such an event is impossible. The conversation highlights the distinction between mathematical models and real-world occurrences, emphasizing that once an event happens, its probability becomes one. The concept of continuous random variables is explored, with participants noting that events with zero probability can still occur. Ultimately, the discussion illustrates the complexities of probability theory in relation to real-world events.
  • #61
quadraphonics said:
Indeed, the cost of including infinity in a number system is that certain basic expressions must remain undefined, when they include infinity. But so what? They're still defined as usual for every finite number, and the expressions where infinity is sensible (like 1/\infty=0) are still well defined.

There is also a finite number that does not work in many basic algebraic manipulations, but is nevertheless included in many standard number systems.

Can you give me an example of a finite number that I can't multiply both sides of an equation by?

I'm not trying to be a brat. I'm just not seeing this.

I would agree that the limit as n -> infinity of 1/n = zero

But I'm having a hard time with this 1/infinity = 0 thing...
 
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  • #62
Archosaur said:
Can you give me an example of a finite number that I can't multiply both sides of an equation by?

No, but there is a finite real number that you can't divide both sides of an equation by :]

Archosaur said:
I would agree that the limit as n -> infinity of 1/n = zero

But I'm having a hard time with this 1/infinity = 0 thing...

\infty, as it is used in the extended reals, is essentially a shorthard for that type of limit expression.
 
  • #63
quadraphonics said:
\infty, as it is used in the extended reals, is essentially a shorthard for that type of limit expression.

I am totally okay with this! I'll sleep easy tonight, thanks!
 

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