So it's a puzzle or perplexity rather than a logical paradox. Fair enough. I think @Agent Smith has something more formal in mind, since he wants it to "break logic".

Why?

The maths works. What more is there — Banno

How you put infinite small pieces together to form a meter? How you know the size of your differentials is right, to not arrive at two meter?

Your question makes no sense. — Banno

:chin: Rounding off a number makes no sense? It's taught in schools, to kids.

How you put infinite small pieces together to form a meter? — Hillary

"Shut up and calculate" - isn't that the physicist's advice?

Exactly, brother Agent! — Hillary

:snicker:

So it's a puzzle or perplexity rather than a logical paradox. Fair — Banno

It's just a logical paradox. It is thought that you can't have infinitesimal small intervals. And that you can't gather them all together to form a finite interval. But it can be done actuslly.

Shut up and calculate" - isn't that the physicist's advice? — Banno

Not mine. I like to know what is actually computed.

You just went back to square one again. I give up.

Have a chat to @Metaphysician Undercover. Sounds a bit like you might have common ideas. He has some odd notions concerning instantaneous velocity you might find amusing.

He has some odd notions concerning instantaneous velocity you might find amusing — Banno

He's right about instantaneous velocity. It's a paradoxical concept. At the fundamental level, the minimum distance is the Planck length.

Update

My thesis is this: If there are true paradoxes,

EITHER

1. We must switch allegiance from classical logic to some version of paraconsistent logic

OR

2. Use Occam's broom and sweep these annoying paradoxes under the rug, ignore them, sequester them in a place where they won't do damage, and the damage can be terrible (vide ex falso quodlibet).

That's all.

You just went back to square one again — Banno

Back? I went forward! What is an infinitesimal?

"A paraconsistent logic is a way to reason about inconsistent information without lapsing into absurdity. In a non-paraconsistent logic, inconsistency explodes in the sense that if a contradiction obtains, then everything (everything!) else obtains, too."

Approaching without being able to touch. — Hillary

:up:

The infinitesimal sequesters the in-between. Squeezes it to death, zeroeing it, annihilates it it by endless compression, an endless go, without a reach, unbounded while bounding. The zero and the infinite meet, get this, for a meeting that never happens.

The very notion of laying infinite infinitely small intervals together is nonsensical. Like the other way round, zero infinite big intervals. — Hillary

Can you think of a polygon with an infinite amount of sides?

Can you think of a circle?

An 10 cm diameter polygon with 1 trillion same length sides might look quite like a circle, but still isn't a circle.

Sorry for butting in, but I don't think people would say such a thing as an infinitely sided polygon = a circle. However, place them side by side and you would be confused which is the polygon and which is the circle, oui?

That's the deal my dear. — Shakeera

Like I mentioned earlier, if we can't have chocolate, by god we'll have something chocolatish!

Heaven!

Sorry, no can do!

Heavenish then!

Check back in an hour!

really just playing with language — T Clark

You are taking my quote out of context.

Perhaps I am not a (real) thinker, but all the excitement about paradoxes goes over my head. I just can't see how they have any practical meaning. — T Clark

Why should they have practical meaning in the first place? But to give a practical example, the twin paradox has significant practical impact to future generations taking a retour trip to Proxima Centauri.

I explained why you are incorrect. You are terribly mixed up and you don't know what you're talking about. And you add additional confusions and misinformation with each post.

the set theory based axioms of mathematics allows Russell's set to, well, exist — Agent Smith

Let's select that quote in particular. It is pure misinformation. ZFC, which is the common set theory for mathematics, is formulated so that it does not allow the usual proof that the Russell set exists, and no one has shown that ZFC does prove that the Russell set exists.

The existence of the Russell set was proven using unrestricted comprehension. But ZFC does not have unrestricted comprehension.

You should inform yourself and stop egregiously posting misinformation.

I explained why you are incorrect. You are terribly mixed up and you don't know what you're talking about. And you add additional confusions and misinformation with each post. — TonesInDeepFreeze

:snicker: A thousand apologies.

Cantor's diagonal argument uses negative self-reference, proves by reductio ad absurdum — ssu

The diagonal argument does not require reductio ad absurdum. And 'negative self-reference' needs a definition.

The diagonal argument is constructive and intuitionistically valid. Though it makes use of an ingenious technique, that technique relies on no logical or mathematical principles that are not common elsewhere in mathematics. Indeed, even without the assumption of infinity, the diagonal argument would still go through as couched in terms of "potentially infinite" processes rather than infinite sets.

axioms don't have to be explained — ssu

Sure, but it is famously the case that certain mathematicians and philosophers do explain the axioms and give justifications for them.

Yet as we don't take as an axiom that all numbers can be well-ordered — ssu

The axiom of choice implies that every set has a well ordering, thus, in particular, the set of real numbers has a well ordering.

A thousand apologies. — Agent Smith

As your posting history suggests, your thousand apologies will be followed by a thousand more of your egregiously misinformational posts. One only has to sit back, have a cup of tea, and wait for the next one.

infinitesimals — Hillary

Historically, infinitesimals were not given a rigorous treatment. However eventually non-standard analysis was devised in which infinitesimals are constructed with the ordinary set theoretic axioms.

As your posting history suggests, your thousand apologies will be followed by a thousand more of your egregiously misinformational posts. One only has to sit back, have a cup of tea, and wait for the next one. — TonesInDeepFreeze

I'm sorry if you feel that way. What exactly is wrong with what I said?

There's very little original material, which I feel bad about, to critique. You should talk to Russell, Whitehead, Frege, et al. Not to me and since you are accusing me of misinformation, I'm somewhat inclined to believe you don't know what you're talking about.

What exactly is wrong with what I said? — Agent Smith

I said exactly what is wrong with what you said just a few posts ago! And I explained also in posts yesterday. And from months ago I've explained why various of your posts are confusion and outright misinformation.

I said exactly what is wrong with what you said just a few posts ago! And I mentioned also in posts yesterday. — TonesInDeepFreeze

You're just fooling around. Sorry, not interested, I'm not in the mood to play your silly games. Good day.

silly games — Agent Smith

Explaining that ZFC does not have unrestricted comprehension that yields the existence of the Russell set is not silly game playing.

:roll:

Good. You are at your most eloquent with emojis.