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### Re: Does infinity exist?

Posted: Sun Jan 27, 2019 3:26 am
Ecmandu wrote:Convergences add a magic infinitesimal to round off.

Untrue. It took 200 years, but mathematicians finally figured out how to banish that kind of imprecise thinking. The theory of limits is perfectly logically rigorous and does away with magic infinitesimals.

Ecmandu wrote:When dealing with infinity, the odds of picking the correct number (that an infinity number generator will pick, or bob next door) isn't 0.0...1. When it converges at infinity, the odds are exactly zero percent.

Untrue as I pointed out. You can't put a uniform distribution on a countable set. That's because of the axiom of countable additivity, explained in the probability link I gave you earlier. If the probability of picking each of 1, 2, 3, ... is zero, then the sum of those probabilities is zero. Yet the probability of picking SOME number is 1 as you noted. Therefore we can NOT put a uniform probability distribution on any countably infinite set.

Ecmandu wrote:Convergences work both ways, not only magically adding the infinitesimal, but subtracting it as well.

Simply not true. There are no magic infinitesimals in the real numbers.

### Re: Does infinity exist?

Posted: Sun Jan 27, 2019 4:16 am
wtf wrote:
Ecmandu wrote:Convergences add a magic infinitesimal to round off.

Untrue. It took 200 years, but mathematicians finally figured out how to banish that kind of imprecise thinking. The theory of limits is perfectly logically rigorous and does away with magic infinitesimals.

Ecmandu wrote:When dealing with infinity, the odds of picking the correct number (that an infinity number generator will pick, or bob next door) isn't 0.0...1. When it converges at infinity, the odds are exactly zero percent.

Untrue as I pointed out. You can't put a uniform distribution on a countable set. That's because of the axiom of countable additivity, explained in the probability link I gave you earlier. If the probability of picking each of 1, 2, 3, ... is zero, then the sum of those probabilities is zero. Yet the probability of picking SOME number is 1 as you noted. Therefore we can NOT put a uniform probability distribution on any countably infinite set.

Ecmandu wrote:Convergences work both ways, not only magically adding the infinitesimal, but subtracting it as well.

Simply not true. There are no magic infinitesimals in the real numbers.

Let's say I'm not even doing it as a function of 1/3...

Let's say I have a paper with the lines.

On each line I start

.3...

.3...

.3...

And I do this forever.

You're trying to tell me that it equals one without a magical floating point?

I'll start right now, and live forever just to prove you wrong.

What I think happened after 200 years (and you never gave me a link). Is that mathematicians figured out how to explain how to give hocus pocus legitimacy through bullshit

Inferential proofs are the best we have.

I know if I write those threes forever, that a 4 will never come up, even though I don't actually do it.

Just like you know that the counting numbers are a well ordered set, knowing that you can't count them all

### Re: Does infinity exist?

Posted: Sun Jan 27, 2019 4:43 am
Ecmandu wrote:I'll start right now, and live forever just to prove you wrong.

Then you'll have time to read and understand this.

https://en.wikipedia.org/wiki/Convergent_series

If I forgot to link the probability axioms earlier, here they are.

https://en.wikipedia.org/wiki/Probability_axioms

Pay particular attention to axiom 3, countable additivity.

By the way, on the general subject of the use of infinity in science ... the foundation of probability theory requires infinitary math, as you can see from that link. And probability is the basis of huge amounts of physical and social science. It's all based on Kolmogorov's axioms, including countable additivity. I should add that to my list of examples.

### Re: Does infinity exist?

Posted: Sun Jan 27, 2019 6:22 am
wtf wrote:
Ecmandu wrote:I'll start right now, and live forever just to prove you wrong.

Then you'll have time to read and understand this.

https://en.wikipedia.org/wiki/Convergent_series

If I forgot to link the probability axioms earlier, here they are.

https://en.wikipedia.org/wiki/Probability_axioms

Pay particular attention to axiom 3, countable additivity.

By the way, on the general subject of the use of infinity in science ... the foundation of probability theory requires infinitary math, as you can see from that link. And probability is the basis of huge amounts of physical and social science. It's all based on Kolmogorov's axioms, including countable additivity. I should add that to my list of examples.

Axiom: if I only count threes forever, there will never be a 4

Your only possible argument is that you haven't counted 3 forever, so you can't know.

That's why it's called an inferential proof.