.999... = 1

[StephenB]

Further proof (as if it was needed), that pizza solves all problems... including whether .999 = 1.

No, you cannot have a piece of ours. Go get your own.

Can I please just have a third of your third? That's only .11111111111

It's a bit more than that, actually, because I will win the game of risk and get the bigger piece - the piece that is 0.000...01% bigger than the other pieces.

[thegreekdog]

Further proof (as if it was needed), that pizza solves all problems... including whether .999 = 1.

No, you cannot have a piece of ours. Go get your own.

Can I please just have a third of your third? That's only .11111111111

It's a bit more than that, actually, because I will win the game of risk and get the bigger piece - the piece that is 0.000...01% bigger than the other pieces.

Oh, actually, I'll just have a third of the piece you win when you beat jones at risk. That's a siginificant amount of pizza, right?

[Doc_Brown]

"people that use flawed logic or poor notation to conclude that .999... = 1 pose no major problems to mathematics as a whole."
No, flawed logic. Nothing wrong with that.

I don't think I was very clear there. What I was trying to say was that misapplication of rules is far less of a problem to me than to claim that the rules are completely invalid. Anyway, let's set that aside.

This just goes to show how we don't really grasp the idea of infinity. We can talk about it all day, but we understand a beginning and an end. We understand finite.

I don't fully disagree that as finite beings we can't really grasp the infinite. However, we do have some sense of it. For example, suppose for a moment that our universe is finite (physicists generally agree that it is but are still trying to define the geometry of it as I recall). If it is finite, then it has an end. Maybe it's just me, but I want to know what is beyond the end of the universe! I'm perfectly happy with a finite earth and a finite space around earth, but somehow I'm not content with some limitation or end to everything beyond which there is nothing. I'm not claiming this rebellion against a strict limitation to the finite equates with an understanding of the infinite, but only a sense thereof.

But let me take this a different direction. Even if no one can fully understand the infinite doesn't mean that no one can make full use of the infinite in various settings. Try this: What are imaginary numbers? Can you really wrap your mind around them and understand them? Where are they? What are they? I don't think I could give a really good definition of them aside from defining them as 2-dimensional numbers of sorts or explaining where they derive from. And that even though I use complex numbers on a daily basis in my field and am very comfortable with them.

You used a lot of limits and the concept of infinity in your discussion.
Anyways, limits are approached. They are never reached. Right?
When we say "the limit of A is equal to B" we are not saying "A is equal to B".

Actually, if A is a continuous and bounded function in the neighborhood of c, then "the limit of A at c is equal to B" actually does mean "the value of A at c is equal to B".

[nippersean]

Not pizza related so I may be off topic but I've spotted a flaw in the Doc's analysis.

If you can't go further than infinity number wise, explain this and stay fashionable

"To infinity and beyond!" - Buzz Lightyear

[sully800]

"To infinity and beyond!" - Buzz Lightyear

An absolutely excellent point nippersean.

[Army of GOD]

Not pizza related so I may be off topic but I've spotted a flaw in the Doc's analysis.

If you can't go further than infinity number wise, explain this and stay fashionable

"To infinity and beyond!" - Buzz Lightyear

Buzz Lightyear is God, which enables him to do anything.

[StephenB]

Buzz Lightyear is God, which enables him to do anything.

I thought Buzz actually existed.