Originally posted by Thales2I'll stop posting in this thread if you can continue it in the spirit it is going in with no serious errors, in a way that ultimately characterises the reals as a field with the same cardinality as the power set of N, on one hand, as a complete metric space on the other. Since this thread is for BDN's edification, you also have to include some discussion along the way about which properties are basically algebraic and which belong to the realm of analysis, and what this somewhat nebulous distinction means. Finally, you have to summarise this discussion by showing that you have essentially encapsulated the real numbers in your construction, by showing that every complete ordered Archimedean field is isomorphic to the reals.
How about playing some chess and cutting the cackle on a subject about which you seem to be more confused than most.
This must all be done in a way that assumes very little prior knowledge and is generally clear to the satisfaction of Bosse de Nage, who is very capable but new to these ideas and who asked for this thread. Also, the discussion must evolve in a way that addresses questions that are asked. Thus while these are quite standard ideas, you may find yourself making nonstandard arguments in the interest of clarity.
If you can continue this thread in this manner, by all means do so. If not, then f|_|ck off, troglodyte.
24 Apr 07
Originally posted by ChronicLeakyWord!
I'll stop posting in this thread if you can continue it in the spirit it is going in with no serious errors, in a way that ultimately characterises the reals as a field with the same cardinality as the power set of N, on one hand, as a complete metric space on the other. Since this thread is for BDN's edification, you also have to include some discussi ...[text shortened]... continue this thread in this manner, by all means do so. If not, then f|_|ck off, troglodyte.
24 Apr 07
Originally posted by ChronicLeakyhaha... i haven't heard someone being called a troglodyte for years!!!
I'll stop posting in this thread if you can continue it in the spirit it is going in with no serious errors, in a way that ultimately characterises the reals as a field with the same cardinality as the power set of N, on one hand, as a complete metric space on the other. Since this thread is for BDN's edification, you also have to include some discussi ...[text shortened]... continue this thread in this manner, by all means do so. If not, then f|_|ck off, troglodyte.
25 Apr 07
Originally posted by StarrmanIt's a pity you don't have anything more to contribute than nonsense. But at least you are a good example of person suffering from racism on the brain.
Hahaha, is this going to be another of your ridiculous claims that you can't substantiate? You do realise this is a forum, designed for posting in? It's a shame you don't have anything to contribute to a conversation other than racist cackle and yet I imagine you expect people to read what you write.
25 Apr 07
1 edit
Originally posted by ChronicLeakyI prefer to rely on the validity of Einstein's field equations and the power of the metric tensor so defined to delineate the curvature of space-time which provides a more satisfactory theory of gravity and the cosmos than did Newton's theory although the latter is, of course, perfectly adequate to explain moving co-ordinate systems which travel at speeds which are small compared with the speed of light.
I'll stop posting in this thread if you can continue it in the spirit it is going in with no serious errors, in a way that ultimately characterises the reals as a field with the same cardinality as the power set of N, on one hand, as a complete metric space on the other. Since this thread is for BDN's edification, you also have to include some discussi ...[text shortened]... continue this thread in this manner, by all means do so. If not, then f|_|ck off, troglodyte.
I am more than happy to continue this thread in this manner but should still like to see what sort of fist you make of chess playing since you have chosen to use a chess site to introduce BDN which Bertrand Russell debunked over 50 years ago.
25 Apr 07
2 edits
Originally posted by Thales2This thread is not about physics. Bertrand Russell didn't "debunk" any of this -- it's all consistent with Zermelo-Fraenkel set theory and none of the usual fiddly bits of the foundations of mathematics have shown up yet, although they will (this discussion is likely to invoke the axiom of choice, for instance).
I prefer to rely on the validity of Einstein's field equations and the power of the metric tensor so defined to delineate the curvature of space-time which provides a more satisfactory theory of gravity and the cosmos than did Newton's theory although the latter is, of course, perfectly adequate to explain moving co-ordinate systems which travel at speeds wh ...[text shortened]... chosen to use a chess site to introduce BND which Bertrand Russell debunked over 50 years ago.
While Russell did, quixotically, attempt a very complete formalisation of mathematics, the problems that arose were not problems with formalisation in general but, in a sense, with the scope of his project. Those problems will not be encountered here; ie we're not going to bump into any undecidability unless, at the end, BDN wants to see something undecidable, in which case I'll try to build an example in this context. Such a thing would be very pathological.
The first part of your post is laughably irrelevant. I don't post PMs in public, but perhaps BDN can post the PM he sent me containing the question which motivated this thread, and you can answer it in terms of Einstein's field equations.
That this is a chess site is also irrelevant, given the diversity of topics discussed in the forums with which you don't seem to have any trouble. Go back to Moominland, you troll.
EDIT I decline your suggestion that I play some chess, since I have no interest in it.
25 Apr 07
Originally posted by Thales2You're the only one suffering from anything to do with racism, namely your persistence that it is acceptable.
It's a pity you don't have anything more to contribute than nonsense. But at least you are a good example of person suffering from racism on the brain.