Thus we have found problems in such a framework.

Proof that 0.89'1 = 0.9 — Real Gone Cat

(Using the apostrophe for '...')

for any x an y,

x'y

doesn't stand for an real number expansion.

Okay, I get it. You're trolling.

As with other debates we've had on TPF, we find philosophy majors trying to bring the wishy-washy terminology of philosophy into a math discussion. Infinity is not understood as a math concept, but as a poorly defined common-language concept. :roll:

I am not. Set theory is self-limiting in the way the theory is formulated.

Define 'self-limiting theory'.

Yeah, I couldn't figure out how to indicate repeated digits. The underscore also seems to work if we agree on usage.

Very simple Tones. A theory that is not flexible enough to allow for operations which would render the theory useless.

Then this is also not new but the old re-formulation of Xenos Paradox — Deus

Which one? Be specific.

(Hmm, coming up with your own definition of infinity ... is this MU ?)

Dichotomy Paradox

'flexible enough', 'deal with operations', 'render useless'.

Not even philosophical, let alone mathematical.

Deus is a crank troller.

Better a than a drunk troller.

Happy for any label at this point. However as a logician yourself give yourself the imaginative prowes to scrutinise the above statement and where proof is warranted … provide it.

I could simply call you an unimaginative logical troll by the same token.

But I won’t.

Oh, I see. So you don't believe that an infinite set can be dense. Got it.

We speak different languages.

(And I gotta hit the hay. TIDF, have fun.)

Also tones your custom way of insulting is to belittle the other guy by calling them either troll or crank but here you’ve basketed the two together.

The point is not to insult, but rather to flag the situation. Usually cranks are not trolls, since they are sincere, though horribly self-misguided. But I take you as a troll since you don't even offer arguments but just simple flippant nonsense.

I understand you better. This then appears to be crank to crank communication at its finest.

https://www.memedroid.com/memes/detail/3284903/Clown-to-clown-communication

The point is not to insult, but rather to flag the situation. Usually cranks are not trolls, since they are sincere, though horribly self-misguided. But I take you as a troll since you don't even offer arguments but just simple flippant nonsense. — TonesInDeepFreeze

This is unbecoming of a Logician Tones. First you called me a crank troll but in the above statement I’m only referred to as troll.

Which is it ?

drunk troller — Deus

A teetotaler can't be a drunktroller.

a logician yourself — Deus

I'm not.

First you called me a crank troll but in the above statement I’m only referred to as troll. — Deus

Both.

A teetotaler can't be a drunktroller. — TonesInDeepFreeze

False premise.

Premise presumes to know about the subjects drinking habits.

Who is the crank now ?

I didn't know whether you're talking about yourself or about me. (And I couldn't resist the wordplay.) In any case, if your point is that you're better at least for not being drunk, then congrats.

If I'm in the mood, I'll give you a second chance. — TonesInDeepFreeze

Fair nuff.

my notation of putting a digit after the repeating term is an interesting way of potentially representing an infinitesimal
— keystone

That is more nonsense. — TonesInDeepFreeze

I agree that as a number it's nonsense...but I believe so are infinitesimals. This is the whole essence of my argument after all. I'm not going to defend infinitesimals nor am I interested in debating the validity of non-standard analysis. But I can certainly write a program to output digits corresponding to 0.891. It's just that that program can never be executed to completion so it would never reach a moment where it would output a 1 digit.

I’m talking about the premise:

A teatotaller <> drunktroller

Your mistake in coming up with the above argument was to presume the subject was drunk from the predicate.

nor am I interested in debating the validity of non-standard analysis — keystone

Infinitesimals are rigorously handled in non-standard analysis. It's not a question of validity.

A teatotaller <> drunktroller — Deus

I don't know what '<>' is meant to symbolize. If it is for some form of equivalence, it's the opposite of what I said. No teetotaler is drunk.

<> means does not equal. A revaluation of facts and reality is required on your part

Infinitesimals are rigorously handled in non-standard analysis. — TonesInDeepFreeze

Please back this up before I declare it a nonsensical flippant assertion.

You think it is incorrect to say that no teetotaler is drunk?

Refer to the subject of non-standard analysis in mathematical logic (starting with Abraham Robinson), or, with a different method, internal set theory. You may consult many a book or article. Probably many articles on online.