Can the probability of an event ever be exactly zero?

[Archosaur]

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...

 

[quadraphonics]

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 :]

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.

 

[Archosaur]

$\infty$, 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!