jgill

Suppose your space is the interior of a unit square in the Euclidean plane and A, B, C, and D are points in that space. Please demonstrate such an alg...

What is a "list of any one real number"?

Sometimes it's all hat and no cattle. :roll:

Wouldn't that be tantamount to counting them? A Turing machine algorithm?

When one is young ten minutes may seem like an hour, but when one is old one may think ten minutes have passed when, in fact, an hour has. In a perfec...

Each irrational number is an "idea", so this process cannot exist. Complex numbers and complex variable theory are more than simply doing math in two ...

And thus we finally learn why we assume the world is mathematical. It's been a long journey, but we have reached the end and may celebrate. :roll:

Not really a "theorem", but entertaining speculation. However, discussing these ideas gets one nowhere. Train to become a Lucid Dreamer or follow the ...

Whoops! I misread this as "The Impact of the Natural Athlete . . ." and I thought, sounds interesting and a discussion I had not been aware of. Nevert...

Yes. Pitiful isn't it? I feel so ashamed. :cry:

Generally speaking this is not entirely incorrect regarding numbers. Euclid's Elements - first four books, basic point-set topology, elementary geomet...

Infinite causal chains and the beginning of time All your concerns will be addressed here. :cool:

Metaphysician Undercover has posted numerous times on this issue. He should chime in.

Oh oh. How embarrassing. Guess I qualify. :yikes:

Having been in the math game for sixty years I feel deprived not meeting such a colleague. I am sure had I done so I too would have chuckled. :cool:

Perhaps a "professional philosopher" would comment on this. Heloooo out there . . . do any such members exist? Please speak up. :meh:

Hopefully this thread can go back to its original focus. Sorry for the diversion. :sad:

Fair enough. When I speak of a topic being "beyond me" it's a cop-out for not having the mental energy at my age (83) to study it, or just a complete ...

58,220 American casualties of the Vietnam War. Three assassinations of US leaders, including POTUS. Rioting, murders of black civil rights participant...

Sorry. Nit-picking here. But how can something change from what it would have been? :chin:

Nice art works, Bob. Welcome to the forum. :cool:

Higher education is under considerable pressure from several different directions. Even before the pandemic hit the public attitude was shifting away ...

Really? I've taught analytic geometry, the calculus sequence, advanced calculus, intro to real analysis (grad), point set topology, statistics and pro...

Let me think about this. I wrote and posted a note on complex time recently that expresses a "real" and an "imaginary" time variable. But not in the w...

What is upsetting you? I have simply stated something I haven't done. There are no unstated jabs at modern mathematics. And yes, I am curious to see w...

From Wikipedia: "The strong, classical view assumes that the 'objects' studied by metaphysics exist independently of any observer, so that the subject...

I've never come across, nor contemplated tracing the proof of something like the fundamental theorem of calculus back to its set theoretic roots. As I...

It seems to me your "therefore" does not logically follow. The "substantial difference" requires a temporal distancing. I suppose you discard elementa...

But what is an "object"? And what is a "metaphysical object"? Is there an overlap? :chin:

As an old retired mathematician not conversant with contemporary set theory, could you clarify your recent posts by explaining how they relate to comm...

Not only intuitionists (who would require an actual construction), but other practitioners as well. :cool:

No relation. Your description of a "tipping point" in physics caused me to see certain neutral fixed points in complex dynamics from that perspective....

Not sure you are saying what you mean to say, here. :chin:

The Peace Corps, maybe? Or some other overseas volunteer services. Sometimes those experiences can be very gratifying and clarifying.

Sorry, we must be talking past one another again. I have no idea what you are saying. Here is a parabolic LFT having a neutral or indefinite or indiff...

Sorry, but this sounds like the worst possible reason for enrolling in graduate school. Probably guaranteeing dropping out. Why not join the military ...

In the world of pure mathematics, a vector field in the complex plane describing a function F(z) having an "indifferent" fixed point a=F(a) might show...

I like this (from Wikipedia) illustrating AC: "Bertrand Russell coined an analogy: for any (even infinite) collection of pairs of shoes, one can pick ...

Nice defense of the AOC ! :cool: I think that those who spend time studying set theory and foundations have a much deeper appreciation for those subje...

OK. Thought you meant rolling along its circumference.

Wrong. It's a cycloid. Far more complicated than a simple sine wave, which it resembles superficially. :roll:

So are sensations and emotions part of the "truth" of the universe? Are they metaphysical, like String theory with its mathematical context? I remain ...

But not entirely, as seen in applications of non-Euclidean geometry. Perhaps there is a "mathematical universe" behind the physical one we see and a m...

And that presumably is what metaphysics is all about. Or is it? :chin:

That's what I would have guessed.

Stanford has a Metaphysical Lab in which an algorithm generates "abstract objects". I have commented that Leibnitz's mathematical infinitesimals may b...

Life goes to infinity? Perhaps explain the diagram.

Two diamonds have the same value, but are not the same. They are equal in value. They appear equal when viewed without high magnification. Just babbli...

From Zen: Form is emptiness and emptiness is form:chin: .

True enough. But they may not be aliens. :cool: