jgill

What an exciting thread this has been! Never a dull moment as we delve into two thousand year-old mysteries. :chin:

If you are thinking of a line segment between points A and B, then philosophically there really is nothing there - its merely a hypothetical path in E...

:up:

Certainly you have two infinite lines. And each line has the cardinality of the reals. Also, both lines, together, have that cardinality. And so on. B...

Are you talking about a single infinite line being somehow countable? Like the points on the line? Or are you talking about the set of all infinite li...

Great crime series on Netflix from Brazil: "Good Morning, Veronica". There have been some wonderful, tough female lead characters lately.

You have reached an absurd conclusion. Of course there can be "two lines". Any finite collection of lines is clearly countable. And there are countabl...

I'll say. Go deeper: Countable An infinite line is a line, therefore, I suppose, a "unit". But they can't be counted since the points in the Euclidean...

Sorry if I awoke you too abruptly from your nap. :cool:

By Jove, you're getting there! Two points do indeed determine a unique line segment joining those points, But there are lots of line segments includin...

Just checking in. 413 posts and still no consensus on what "real" means. You are a disappointing bunch. :sad:

Taxicab Fun I don't know what you're talking about. Provide an illustration, please. Show me how you count them, 1,2,3,4,5,...

So, if I have a countable collection of lines, they are countable? I suppose that's a step in the right direction. If it's in a countable collection t...

Set theorists and foundations people might be interested in such distinctions, but for me infinity simply means unbounded. Going back millennia to stu...

Oh boy, here we go again . . . :roll:

Well said, as usual MU. At 85 turning a heavy page can irritate an arthritic finger . . . but worth the effort.

Agree. After almost 200 posts . . . :roll:

And there are so many, many of those. My math genealogy alone goes back to Karl Weierstrass (1850s), one of almost 40,000 descendants of that gentlema...

I just took a moment doing what I do to read this post, and now I feel so guilty. :cry: You have no mercy, MU.

0=\{\text{ }\} ? :roll:

Picky picky. Of course they don't. But in the spirit of this discussion they could. There are enough ambiguities in math to satisfy MU. Take f for exa...

This discussion revolves around the use of the word "opposite" in math. Apart from integers - the focus here - it arises in discussions of geometry, l...

A sort of "Cancel Culture" of TPF.

A curious statement. All the years I've practiced math I can't recall using "opposite" in this way. But I suppose some do. Indeed. Centuries ago.

Proof of something like time travel would be more appealing.

Word games full of sound and fury . . . :roll:

Any luck there?

MU makes a good point regarding some highly abstract mathematics. I'll tell the story again of a PhD student writing a fine looking thesis about a cer...

Thanks for adding to my vocabulary. I had to look up "eschaton" to see what in the world you are talking about. Now I'm glad I had no knowledge of thi...

Usually the concept of work relates to a change of energy, kinetic or potential. When an object follows a path through a force field, if that field is...

:up:

Richard Muller, physics professor emeritus at UC Berkeley, states that energy is the most difficult concept to understand in the basic physics curricu...

Mathematical Schemes is an example of current levels of abstraction. If I were an algebraist or topologist I would probably see the values therein. Th...

At the lower level of technicians perhaps, but I doubt it since thinking involves both hemispheres. Advances in science require imagination, which cer...

Well, this has happened in mathematics as specifics have given way to greater and greater generalities, an approach that has brought together various ...

Einstein had taught himself differential and integral calculus by age 15, and had a teaching diploma in math and physics before the patent office job....

Probably you mean Giulio Tononi. His Phi function is untenable.

Reminds me of the movie Good Will Hunting in which a janitor solves a ridiculously difficult mathematics problem while erasing a blackboard each day. ...

A non-differentiable manifold. Live with it. :brow:

True enough. I don't have a Professional Degree in metaphysics. But I respect those who do. :cool:

Bless you, young man! :fear: I only meant I could not find where he might have said this. Nit picking. :wink:

They still search for fire they can breathe.

Breathing fire is vastly overrated. Exploring the math can do that job. No need for unicorns.

Really? I can't seem to find a reference. Do you have one handy?

That would be my guess. Were I a physicist I would be in that camp. Actually, I probably wouldn't care one way or the other.

Paul Erd?s Did you have this sort of thing? \sum\limits_{{}}^{{}}{\prod{{}}} (I use that all the time) Have fun. It looks dreadfully unappealing.

If you search for "real" in your Schaum's Outline of Quantum Mechanics you will find nothing, save mentions of the real number system. "reality" is in...

It looks like progressives vs regressives. I guess I don't see the purpose of it.

I was thinking only of a more mundane application of S's equation, with wave packets and probabilities of a particle being at a particular place at a ...

Breathe fire :cool: