fishfry

I can't read you the news. I don't think you and I live in the same reality if you believe what you wrote.

I'm still concerned about that screwdriver ... Perfectly standard. By the definition of a metric space, right? Also perfectly standard. Yes ok. Yes th...

Just posting the link since SEP has a lot to say about holes. Guilty as charged on he rest of it. Guess I'll go crawl back into my, uh, hole.

https://plato.stanford.edu/entries/holes/

Wow. Man. I read your post. I have no idea what you're talking about. A metric space has a metric. Some topological spaces are metric spaces. But a to...

Some people in the public square these days would burn you at the stake for arguing for equality of opportunity versus equality of outcome. And for ex...

I agree it's about a right-open interval. We have 1/2, 3/4, .. in (0,1). We can adjoin 1 to work in (0,1]. But I'm not talking about anything else! Th...

Of course it's not a physical possibility. If by metaphysical you really mean physical, then it's not a metaphysical possibliity. But clearly we human...

Should you abbreviate it, I might have a chance at reading it. My first impression -- again, forgive me, but I'm finding some virtue in just telling y...

Is there a name for the logical fallacy that "P is repugnant, therefore not-P." That happened with non-Euclidean geometry. A priest worked out the imp...

If only. The new word is "equity" and it DOES mean that everything should be the same. Equality of outcome and not just opportunity; and if outcomes a...

Yes it does. If I define the first three elements of a sequence, like 3, 12, 84, what number comes next? Mathematically, it can be any number at all. ...

Standing by for something specific. And if it's not too much to ask, can you keep it short? I myself tend to write long-assed posts. I should take my ...

Make everyone an impoverished slave and feed them all the same bowl of gruel everyday. That's the problem with "equality." If you have a system that a...

42. Can you argue otherwise? The final state is not defined. It can be anything we like.

This is just the lamp story with three states. The answer is that the sequence 0, 1, 2, 0, 1, 2, 0, 1, 2, ... has no natural completion or limit. So i...

I did not get a mention for this post, does that happen sometimes? Maybe I just missed it. As I have been explaining in this thread, you can conceptua...

I await your next missive with both curiosity and trepidation. Is it wrong for me to encourage you on the one hand, then give you a hard time the next...

I have never expressed, nor do I presently hold either of those beliefs. I cannot take responsibility for the execrable state of math education, or fr...

You've just described the ordinal \omega + 1, which has as one representation the sequence 1, 2, 3, 4, 5, ... , and another more familiar representati...

The lamp and staircase scenarios are physically impossible. What law of logic makes them logically impossible?

There is no physical process. There's a fictional process that doesn't obey the known laws of physics. In what sense does anyone think the staircase o...

Nice to see you again @jgill, and thanks.

This is an interesting argument. I have some issues with it. First, I should note that infinite divisibility is a weak condition. The rational numbers...

Cute. In this case I agree that it's natural, in the sense of preferring continuity, to say that the final (ie limiting) state is resting on the table...

Thanks for clarifying that for me. I don't see a paradox. All I see is a lack of understanding of mathematical limits. Consider the sequence 1/2, 3/4,...

You seem to be under the impression that Robinson's hyperreals define a unique smallest positive infinitesimal. This is false. If h is a positive infi...

The formalisms are wonderfully clarifying of one's formerly fuzzy intuitions. For example the idea of stepping back from the bottom. It's only a finit...

Apology completely accepted. I'm a little hypersensitive in general. No worries as they say. I may have misunderstood a lot because I was focussed on ...

So your point was that if everyone older than you dies, you'd win the argument? Your use of Planck's quote makes not a lick of sense. He was talking a...

Ok I hadn't seen that before. Whatever shows at the end (if that even makes sense) it's certainly finite, since you're adding up finitely many finite ...

I don't follow. In calculus, the sum of an infinite series is defined. According to that definition, the sum of 1/2 + 1/4 + 1/8 + 1/16 + ... is 1. But...

Ok fine. In what sense do you regard Zeno's paradoxes as new ideas? That doesn't make sense.

Depends on if the calculator is required to follow the mathematical theory of convergent infinite series. If yes, 1, If no, then it can be anything at...

I gave the example of the first transfinite ordinal \omega. Any step you talk backward from it lands you on a natural number, from which it's only fin...

What perspective do I have and why on earth are you going on about it like this?

Your argument is that Zeno's paradox is so new and revolutionary that I'm too old to see it? Zeno lived 2700 years ago (5th century BCE according to S...

The lamp violates the laws of physics, so it's not a real lamp. It's only a metaphor for a mathematical puzzle. Why can't it turn into a pumpkin at mi...

Believe so. No chance. Didn't do any good, nobody understood a word I said.

I'm perfectly happy to continue the conversation. I'm only saying that you might be disappointed if you hope to convert me to your degree of passion, ...

No misrepresentation. And why must something happen at the limit? Take this mathematical example. We work in the space (0,1), the open unit interval o...

It's possible that sometimes it is. For example if we flip a coin, that's only epistemically random, in the sense that it's a purely mechanical proced...

Better not to try to subtract the endpoint infinities from each other, The result is undefined. Thanks much. I hear all the cool kids hang out in the ...

Another good question. Yes we could put "negative omega" at the leftward infinite end of the integers. There's not much use for it. The interesting as...

Those are great questions. No. The natural numbers are the positive (or nonnegative, we'll talk about that in a moment) whole numbers like {0?], 1, 2,...

I accidentally wrote this on the wrong thread so I'm moving it over here. I have some thoughts that may be of interest. The staircase problem is calle...

Oh well then now I'm thoroughly confused. It's fitting to be down a rabbit hole, given the nature of the topic. ps -- Oh I see what happened. I posted...

Oh YOU messed the threads up? I apologize to the moderators, whose names I have taken in vain. :-) said jokingly of course

moving this post about omega sequences to the stairway thread, where it belongs

Wow this was a good post. I understood everything you're saying and I agree with much of it. Even in parts where I disagree, we're still talking about...