Recent content by andrewr

OK, yes, good... Sets can be arbitrary sequences, or unordered, and all we need is some arbitrary rule to decide which elements are successors, and predecessors of others, to be able to list them out as you have done. So you would have a rule that you want to call "funny" which determines why...

No, I'm not making up words ; so your "if" is false. I was at most given a bad piece of information by a mathematician with a degree, and if I could edit the opening post -- I would have done so. But the time to do so has expired... so my only two alternatives are to start a new thread, and...

I'm only interested in sets which I think should be of size aleph naught, so I think the answer to your question is "yes": If construction of a set by appending (unioning?) 1 element at a time means "countable", then definitely YES -- otherwise -- no, I don't know how to answer your question...

Good question. That's a place where the things I've been learning about Cantor sets gets very foggy. I find it difficult to keep the terminology straight. I think the phrase "finite unbounded" applies to the characteristic of a set where every element that one can inspect in the set during any...

I've have been taught that the difference between open and closed sets is whether or not the set contains the supremium. At least that's what a mathematician told me, and I am going on trust for he has the degree and I don't. I am also thinking that the supremium of a set would be the element...

I have been looking at the idea of 1:1 correspondence as a method of determining set size/cardinality, and have noticed that the principle allows for inductive proofs, which I think are properly constructed, that can come to conclusions which are clearly wrong under traditional set theory if...

:) I have been trying... and I wouldn't have gotten it with just the information in post #5. :( I was able to work it all the way through, finally, today. Thank you both.

Much better! Yes he did, and a fine job, too! :) However, I still need to solve for the amplitude, A. He gave r and s in terms of divided A; which results in s/r being independent of amplitude. But the equations for s and r, require knowing both x and y; aka phi2, and 1. not just the...

Hi! I'm doing a project with sound, and exploring modulation. I got stuck on an intermediate step ... and can't solve a simple algebra problem. I have a wave, which I know the envelope is a perfect sine wave, and fits the following three equations: A * cos( ph1 ) = knownSlope1 A *...

:zzz: Well, I still haven't found any pictures... esp. human ones... but I stumbled across something I didn't know that is suggestive: Researcher "Barbara A. Bohne" notes in her "morphological analysis of hair cells in the Chinchila cochlea", that across several mammals, the outer hair cell...

Hi, I've been studying the cochlea, and how the hair cells (IHCs) receive sound, and some amplify it (OHCs) ; and am trying to get an idea of the density profile of hair cells acting as a spatial filter. The smallest discrimination in frequency that is positional (not temporal) coded...

It's been over a year... and I finally have some time to pursue it.. although, it might be better to just start over; I figure I'll post here first just to let those who already posted have first whack. As to that comment I made, it's generic. Faraday spoke loosely about "force", "source", and...

Yes and No. I didn't just say QED at the end -- but gave a statement of what was proven. Hence, I can copy that statement to the start of the proof to show what I'm going to prove -- it's sort of redundant; but OK, I can do that. Regarding the mutability of A, which is being constructed, you...

There is a second way that I can answer your question. Georg Cantor is the one who claims 1:1 correspondence means two sets are the same size. He does not restrict, as far I as I can tell -- and I have asked others -- this axiom to infinite sets. He claims that it works for finite sets as well...

I've never heard that every possible mapping function had to be examined, before. My understanding is that listing a single 1:1 mapping between the two sets is sufficient to show they have the same cardinality (I'm presuming no redundant elements); So I am implicitly taking as an axiom, that any...