jgill

What is "evidence" in a metaphysical realm?

How do you propose to pass from a finite line to a circle, say? If you are considering topological transformations, how can you express them? Sorry fo...

Unfortunately, your approach is a muddled mixture of traditional ideas and speculative continua. I think you need to go back to the beginnings of your...

It looks like you simply move the point down the line segment to different (faulty) positions. How does this affect your metric? :cool: Very very few ...

Well, if you were to avoid both metric spaces and variations of the word "topology" it might mitigate what seems to be a questionable attempt to emplo...

On those very rare occasions in which the subject arises I have felt the two to be more or less alike. But, here is what Wiki has to say:

Ditto. So, a continuous deformation takes path A to path B, but inside the ms of path A? Or a new ms of path B? You might illustrate this. I'm curious...

The saddest words of tongue or pen: it might have been.

This is perhaps the second time this oddity from number theory has cropped up on this forum. I knew a tiny bit about it since it can involve elementar...

You speak of a metric space. Precisely what are the "points" in such a space? Then explain the metric you have created giving "distances" between thes...

From the Bleachers: Does \cup (\pi ,\pi +1)\cup \cup (\pi +1,5)\cup exist in your system? Or are you assuming rational numbers only? Is \cup (5,5+\var...

I don't know what you are talking about. You and @fishfry can sort all of this out if he is willing. Good luck.

"In a metric, the distance between two distinct points as always positive." d(,)=0 ? not equal to .

What is "irrational infinity"? Infinite sided die seems like a sphere in 3D. Does magic influence the world around us? Wow, what bizarre powers I wiel...

Not much, I fear. But I stand aside and try not to impede the ongoing discussion between you and @fishfry, who is more familiar with modern math topic...

Not so sure philosopher and critical thinker are one and the same.

You have used this expression frequently. Do you know what you are talking about? Just curious.

Works sometimes. Not always. A brief, concise OP helps.

An exercise in free will. At each n the cube changes from white to black or vice-versa for time = 1-1/2^n. The clock runs out so you are free to say t...

That's no surprise. It is an imaginary contrivance impossible to physically fabricate. Just a thought.

From the bleachers: Hasn't MU spoken of the existence of continua prior to points? What of Bergson's notion of time being fundamentally duration? Perh...

No argument with that. :roll:

For those, like me, who didn't know: Fallacy of the undistributed middle

Pass the popcorn, please. I am sitting in the bleachers watching with interest. :chin:

f(x)=3x+2, f(1)=5 \underset{x\to 1}{\mathop{\lim }}\,f(x)=f(1) Certainly the relationship between time (independent of human control) and physical ste...

But ?

Welcome to the Forum. :cool: How do the drawings on cave walls imply intellectual capacities rather than simply artistic abilities?

:up: Amen :roll:

I hope that works for you. I was a math prof for many years, and at large universities senior faculty might simply give an unsolicited paper to a grad...

I wonder how dynamic systems would function. At each step there would be many options.

Wonder what that 8,500 crossings/day means? Not enough energy to check it out.

I say yes. I predict that in my area, math, there will be computer devised concepts and results beyond human understanding. If simply the length of a ...

Or perhaps the only apparent option to remove the Biden cabal. Don't forget, Joe told immigrants to "Surge the Border", and gave Afghanistan back to t...

Be tolerant and thankful for a furry companion. :cool:

Add The Philosophy of Taylor Swift to the middle school part.

Good for you. Keep it up. When you are very old something may knock you down, then as you try to recover, doctors will find something else. A downward...

I tend to vote more conservative than liberal these days and I object to illegal immigrants having guns.

No amen yet. Still hoping for a different Dem ticket. "Surge the Border Biden" deserves defeat.

If most citizens have the right to gun ownership, what of illegal migrants?

:up: It won't be long before mathematical concepts and results stretch beyond our abilities to comprehend.

Reference?

When it amuses. Keep going. :cool:

I am speaking of the actual science, not peripheral sciences nor philosophy concerning the use of scientific discoveries. Also, I included other kinds...

Says it all :roll:

So, this entire discussion devolves to something I used to teach freshmen.

You guys need to find a bedroom. I'm surprised we others are allowed to witness the proceedings.

:roll: .

Royal Robbins, The American Climber by David Smart (2023)

Agreed. But that philosophy should be provided by the scientists.

I don't see how philosophers looking over scientists' shoulders does any good. The various sciences have their own procedures, with the exception of q...