The set of all logical formulae: Countable or uncountable?

[Speakpigeon]

What I'm getting at "pi is a ratio between 2 different lengths, one of which isn't measurable with a non-transcendental, bendy ruler.

If you can't measure a circumference how do you come up with pi? I would have thought it was empirical.

I can think of several ways to measure a circumference. Create a circle and overlay a string, measure the length. You know me, I'm no mathematician just a simple minded practical engineer....

It's not empirical. There are hundreds of known formulas for pi. Even before computers they were a better way of finding pi than using a tape measure. Here's a smattering...

Yeah, and I would put the emphasis on "better": "they were a better way of finding pi than using a tape measure".

I would guess there a practical limit to the precision of some kind of physical measure of Pi. Well, I think the maths will always beat that, even if there may be a limit to that, too.
EB

 

[Speakpigeon]

Ohh, so the idea was that Pi could be described without using an infinite amount of symbols.

Yes indeed. Like a finite-sized algorithm for calculating that number.

The algorithm is finite but Pi is never actually computed. It's only "computable". Saying Pi is the ratio of circumference to diameter provides the rationale for the algorithm. So the finiteness of the algorithm is already in the definition of Pi.
EB

 

[Speakpigeon]

So, dividing a physical object in 9 equal parts and summing over 6 of them results in a different quantity when you weigh the result in a decimal or duodecimal system of weights?



Google "rational number" and don't come back before you've understood the definition.

No object can be divided into 9 equal parts. You can only get 9 parts that are very close.

I am talking about a specific ratio in base 10.

It is not like anything else.

You can only get approximate equivalencies if you look at other bases since in base 10 it has no final value.

Yes, but it's also true you're not actually there in front of me so it's not like you exist for real.
EB

 

[untermensche]

So, dividing a physical object in 9 equal parts and summing over 6 of them results in a different quantity when you weigh the result in a decimal or duodecimal system of weights?



Google "rational number" and don't come back before you've understood the definition.

No object can be divided into 9 equal parts. You can only get 9 parts that are very close.

I am talking about a specific ratio in base 10.

It is not like anything else.

You can only get approximate equivalencies if you look at other bases since in base 10 it has no final value.

Yes, but it's also true you're not actually there in front of me so it's not like you exist for real.
EB

It might exist.

We cannot say it doesn't.

But it does not exist as we perceive it.

We are not perceiving it. We are perceiving something else.

 

[Speakpigeon]

Yes, but it's also true you're not actually there in front of me so it's not like you exist for real.
EB

It might exist.

We cannot say it doesn't.

But it does not exist as we perceive it.

We are not perceiving it. We are perceiving something else.

???

I don't know, read again?
EB

 

[untermensche]

Yes, but it's also true you're not actually there in front of me so it's not like you exist for real.
EB

It might exist.

We cannot say it doesn't.

But it does not exist as we perceive it.

We are not perceiving it. We are perceiving something else.

???

I don't know, read again?
EB

Your misunderstandings are numerous are tiresome.

You cannot experience me.

I am not something you will every see.

 

[Speakpigeon]

???

I don't know, read again?
EB

Your misunderstandings are numerous are tiresome.

You cannot experience me.

I am not something you will every see.

Sorry, you're not making sense. What is it I misunderstood here?
EB

 

[untermensche]

....you're not actually there in front of me so it's not like you exist for real.

Misunderstanding.

 

[Speakpigeon]

....you're not actually there in front of me so it's not like you exist for real.

Misunderstanding.

That wasn't misunderstanding. It was irony. Something you don't get, obviously.
EB