Recent content by phoenixthoth

I was wondering if anyone knows of what type of law is involved with the terms of service of internet discussion forums. Is it possible through terms of service for a discussion forum to legally own poster's posts? Thanks!

Thanks for that. It looks like Brownian motion is the closest thing to an application of NSA to physics.

Hi PF contributors, Have there been attempts to apply nonstandard analysis to the behavior of photons? For instance, considering the mass of a photon to be infinitesimal. I'm guessing the answer is yes so if you could provide references, I would be much obliged. phoenixthoth

Are there any references online that explain this result differently from how I did it (or almost did it) as I cannot find Hinman's book online?

That in itself is very useful feedback. Thank you. I guess I haven't studied enough set theory because I haven't seen this result before. I'm glad I don't have to reinvent the wheel. I will see if I can find Hinman. We might as well discuss those innacurate things. I don't know if changing...

I was wondering this too. In base Pi, 10 is Pi so since Pi is 10 in base Pi, well, 10 looks like an integer! Weird!

I would appreciate any and all feedback regarding this document currently housed in Google docs. Basically, I generalize induction among natural numbers to an extreme in an environment regarding what I call grammatical systems. Then an induction principle is derived from that which holds in...

Here's one that I think is hard: math = ?

Sorry, I meant positive measure.

It's disheartening slightly that when we expand our understanding of what might a mathematical object be, there is resistance to this endeavor. This type of resistance has occurred many times in the history of math. What I find ridiculous is the resistance to opening more doors in terms of the...

Yes, great question. This will dictate how to proceed as what you are trying to prove may basically be directly derivable from definitions.

Suppose for the sake of argument that we look at ZFC with the axiom of infinity removed. http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems#First_incompleteness_theorem http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems#Second_incompleteness_theorem We would...

A polygon with nonnegative area cannot be formed with fewer than 3 points. A polyhedra with nonnegative volume cannot be formed with fewer than 4 points. A hyperspace with nonnegative measure cannot be formed with fewer than n points. What I mean by "3 points" is that the cardinality of the set...

Thanks, though I was really hoping to hear others chime in on what is a mathematical object. I will try there, too

Yes and that's probably true of the process of defining anything: there are atomic words used in the definition. "There is no absolute notion," that is what I am trying to remedy...