# 0.33333333

#### AplanisTophet

Repeating a false claim doesn't count as evidence. Can you explain what you mean?

That couldn't be more false, as it contradict known physics and profoundly misrepresents the nature of physical measurement.
There are only finitely many atoms in the line segment, so finitely many ways to write a line segment, no?
What about line segments that are only $\pi/4$ atoms in length? Since when is the atom the smallest unit of measurement?

#### Maschke

What about line segments that are only $\pi/4$ atoms in length? Since when is the atom the smallest unit of measurement?
How could a number of atoms be a non-integer? Aplanis what on earth are you talking about?

#### AplanisTophet

How could a number of atoms be a non-integer? Aplanis what on earth are you talking about?
I don't know, break one in half and hope for the best? For the negative atoms we'll use anti-matter. I counted in inches though, not atoms like you are, soooooâ€¦ :giggle:

#### AplanisTophet

There are only finitely many atoms in the line segment, so finitely many ways to write a line segment, no?
Why are you implementing the idea that we must be able to write the line segment with only atomic precision (as if even that is possible)?

I could have just said I'm using a language where each element of $\mathcal{P}(\mathbb{N})$ is a sentence of the language representing $\frac{1}{3}$.

The point, for the OP's sake, is that we can represent numbers using whatever notation we want. The numbers are what they are, just like Maschke is who he is (no matter what names I choose to call him). :ninja: #### Maschke

The numbers are what they are, just like Maschke is who he is (no matter what names I choose to call him). :ninja: And no matter how many direct questions I ask you that you pointedly ignore.

#### AplanisTophet

And no matter how many direct questions I ask you that you pointedly ignore. Do you seriously have a question?

No reason we can't have uncountably many formal symbols. Just let each real number be a symbol. I don't know if "symbol" is formally defined anywhere but in logic you can make any set into an alphabet of symbols. Typically the alphabet is countable but in some applications it's uncountable.
FWIW I found a specific reference regarding uncountable alphabets. Here's the link ...

And here's the relevant paragraph. Ok, so there's your answer. Let each one of those symbols you speak of equal $\frac{1}{3}$ and you've got your uncountably many representations of it. #### [email protected]

What about line segments that are only $\pi/4$ atoms in length?
Uh, yeah. So how does that work? You want to show the notation to somebody else no? How does somebody else see this if it isn't made out of atoms? How do you write it down if it isn't made out of atoms?

#### Maschke Do you seriously have a question?
Yes, at least two that you pointedly ignored. One of which is what does pi/4 atoms mean?

Ok, so there's your answer. Let each one of those symbols you speak of equal $\frac{1}{3}$ and you've got your uncountably many representations of it. #### sintan

But decimal notation of fractions is not fundamental to math. It can be dispensed with entirely.
OK this seems a step in the right direction.Any infinitely recurring decimal is simply stricken from mathematical language and always expressed fractionally.
Even on calculators. We may need a linear method of expressing fractions and then forgot the whole decimal system between integers?

#### v8archie

Math Team
Or you could try to understand what recurring decimals actually mean and also the limitations of calculators.

It's rather easier than trying to guess which answers are rational and which aren't.