jgill

Sure. This brings up an interesting question: If two things are equivalent, A<->B, does that mean they represent the same math object? In the example ...

Yes, the similarities don't define the object, however. Is an "object" its' representation picked at random? Or, is there a more metaphysical meaning ...

1. should be interesting. You have density, but then continuity is next. Intuitionism math perhaps. I thought you were defining these lines as continu...

I don't think you will get a reaction from anyone but me until you produce a plan moving forward from your images of edges, vertices and surfaces. Wha...

Now that you've moved into graph theory I suppose I see some sort of a way to move forward by taking a lattice graph over an area and allowing the num...

You have done your imagery very well. I will wait and see what comes next.

Your second figure is bewildering. Maybe go back to 1D and explain the real numbers as you see them. Expressions like k-vertex instead of point are co...

I recall that Sweden allowed large numbers in, then several years later changed its mind.

One more slight digression from the original topic. I have been in this position. Rules of Affirmative Action applied and the dean asked for the top t...

If the government insists on flying in "inadmissible" immigrants, then they should be carefully chosen to benefit the nation in some manner. Doctors a...

I appreciate the graphs you have drawn. You have 2D surfaces that are defined by interiors of edge figures. The surfaces, edges and vertices seem to c...

Framing the conversation in terms of preserving the state or nation. 1. "A failed state is a state that has lost its ability to fulfill fundamental se...

Why resort to graph theory and call a simple line an edge? Is this an effort to enhance an almost trivial concept of line and point? Again, why not go...

Exactly what it was intended to be. How about my previous statement about a mathematician is one who scribbles on paper, curses, then wads the paper u...

Does make you wonder. If this is the real Grinin he may have signed up, then upon reading some of the threads decided to move on. His Wikipedia page g...

OK, you have a line that is indivisible. But it has k-vertices that "cannot be partitioned". Can a vertex be partitioned? Like saying a point can be p...

Although I don't subscribe to mathematics being one object, when one looks at specific areas of the subject one can say that one object prevails, and ...

Sorry, it looks like you are taking a line segment and dividing it into two smaller segments. Then comparing. If you think there is something signific...

True. I hope there is something of interest coming from this discussion. But we've been through metric spaces and topology and now are venturing into ...

True enough. But I keep hoping there is something profound I am missing in all this. :roll:

What structure? A line segment has structure? One line segment has the same "structure" as another? You must see something there that eludes me. But I...

I seem to lack your insight in this example. It appears you simply take a real line and divide it into several line segments by inserting "k-vertices"...

It's just fairly simple BASIC programming that I enjoy creating. I tried Pascal, Fortran, Mathematica, C++, and one or two others, but by the mid 1990...

Retired for 24 years. Lots of things slip by. Hard enough to persist along the lines of mathematical thought I know about.

A big jump in credulity. But OK for the Lounge I suppose.

I wonder if Calculus on Finite Weighted Graphs is the direction you are headed? This is a topic even less popular than mine, with a scant 8 views per ...

Not sure what you mean by actual infinity. Are you speaking of infinity as a sort of number that can be arithmetically manipulated, or infinity as unb...

No I haven't. And I have little interest in Riemann surfaces. I have used MathType for years with Microsoft Word for writing purposes. For imaging, I ...

Somewhat similar, but not quite the same thing. I've never particularly enjoyed solving problems, but rather exploring where certain specific ideas in...

Here's a personal anecdote that may be telling: My PhD class had several women. One dropped out for health reasons, and another was the top student, b...

Perhaps at the more prestigious schools, and maybe at less elite institutions as well. I think I checked on this for Harvard and found such a course, ...

Was it Einstein that said something to the affect that God gave us the natural numbers, all else of mathematics are mans' ? Or something like that. Wh...

In America women make up 25-30% of PhD students. 15-20% of math faculties. Not entirely men. To me this seems like a word game. Describing a theorem, ...

Statements devoid of content? (Frege) I think not.

I've never known a fellow mathematician who would have agreed with this. A mathematical philosopher perhaps. Let's see what @fishfry has to say. I alw...

Math itself is full of systems, like the system of the natural numbers, or the system of addition. So, in a sense, you might say it is a system itself...

If I had to guess where you are headed, I might say that taking a continuum (a line,say) as axiomatic somehow you are cutting it into a fine mesh usin...

Over the years colleges have designed their curricula to suit the levels of abstract thought students can bring to the classroom. Calculus is taught i...

I will be interested in what younger and more agile brains make of this. :chin:

And then straighten out a (continuous) curve and you have a continuum, which the OP argues does not exist. Perhaps you should start a thread entitled ...

When it searches for Adamford.com it goes to your site, but on and off for adamford.com - as you have listed it - it goes to car dealerships. And Goog...

So we begin by defining such curves as "inherently continuous". That seems to solve the problem. Why proceed? Why dabble with sets of points that may ...

From the desk of an old mathematician. For me potency means a function I design that when implemented by choosing a point from its domain produces a r...

When I see a diatribe like this I speculate why its author is so vehement. Why does your website on your bio page list www.adamford.com, a site Google...

And you say you are not a mathematician! :cool:

I have seen up close a corruption of Affirmative Action, and whereas I had thought it reasonable before, afterwards I was reluctant to support it. It ...

You've made your point. Don't rub it in.

For a moment I was thinking q^2<2 normally is q<sqr(2) for positive q, but if irrationals do not exist this inequality is invalid. It seemed to discon...

OK. I used to teach elementary point set topology occasionally but it has been over a quarter century ago. Best for me to avoid this discussion at my ...

Ok. You are disconnecting Q at a point that does not exist in Q. Thought you were restricting all points to Q. Usual approach to this is to assume the...