ughaibu

Well, as you apparently didn't understand anything I wrote, my time too has been wasted. Kindly stay out of this thread.

Yes, I know, and thanks for your patient and thoughtful input. Without worrying about this, consider the following alternative scenario: if I have some formula which generates x for all n such that n>1 and is an integer, if I can prove that for the base case of n=2 then x=1, is the establishment of (n/n-1)>x>(n-1/n) sufficient to conclude that x=1 for all cases?

Sure, as a general statement it's obviously false. The situation here is that a/b=1 by examination for the base case, and both the larger and smaller terms tend to 1 in higher cases. However, the inequality was generated by assuming that a/b isn't equal to 1.

Dont worry about it, I suspected that I didn't have enough and Lawcat convinced me. I think I've found a different way to do it.

I see. Thank you for that, I'll think about it some more.

If I have some fraction, a/b, and an inequality stating that this is bigger than x and smaller than 1/x, and if in my base case a/b=1 and both x and 1/x approach 1 as cases become higher from the base case, do I have sufficient to state that by induction a/b=1 for all cases? The complication being that I arrived at this inequality by assuming that a/b<1, in a word, do I have enough here to say that my assumption that a/b<1 is false?

My point was that this exemplified confusion about dimensions. The limit has no two dimensional component and the one dimensional component, ie the perimeters, were never the same. Archimedes employed a similar construction in proposition 2 of The Method, without the confusion and in a more radical way. The Method hadn't been recovered at the time of Galileo. Were there only two great minds who thought somewhat alike on this matter? And only one discovered a wonderful analogic method that generated exact results.

There's a nice proof, due to Galileo, that all circles have the same circumference. Do you accept that proposition?

Are they?

Those using a japanese keyboard might take issue with this, when I tried experimenting with Latex I found very little correspondence between the instructions and the output.

Could somebody explain the basic mechanism of Papakyriakopoulos' tower argument please.

In such a case zero divided by zero would equal the set of all possible numbers. What happens then?

If endosymbiotic innovations are common and if endosymbiotic innovations regularly lead to new life forms, then one would expect new life forms to arise regularly. Anyway, on this apparent doubt that you have about all life arising from single celled organisms, you claim to be non-religious, so presumably your brand of intelligent design doesn't involve any supernatural craftsmen who can produce multi-cellular life out of the blue. How does your theory account for the existence of multi-cellular life?

Thanks for the lengthy reply. If I understand it, you seem to be saying that "created" amounts to "artificial", "fake", "incorrect", etc, is that the gist?

You're aware of endosymbiosis(?)

This is what you want transitional fossils for?

In which group do you put hyper-dimensional geometry, sets of infinite cardinality, algorithmic randomness, incompleteness theorems, etc?

You're joking, I hope. The cliche is horses. Really, surely everybody came across this before they were ten years old.

The documentation referred to appears, primarily, to be the Bible.

Of course he did:

Yes, I realise that, nevertheless, if my argument in post 20 is sound, I think normality would be a problem for some non-repeating, non-terminating numbers. I suspect the problem with my argument is premise 4, that only finite sequences appear in the expansion, whereas the power set of aleph zero includes infinite sequences. However, I dont see why the expansion can not contain sequences of length (cardinality) aleph zero(?) Anyway, thanks for your reply.

Does this article meet the requirement? Borel Normality and Algorithmic Randomness # - CiteSeerX

Go on strike, stage a sit-in, or a love-in, or a picnic with beer and pickles by the river side, get a new job (as Tormod's boss), but keep your priorities straight, play is more important than work.

Me? I know it as a Hampton Court spider. There's no Google result so I cant check the latin name with yours.

As I understand it, all spiders are venomous but only a few can pierce human skin. So, if you have open sores, I guess any house spider could be unpleasant. Trivia question, what is the common name of the UK's only capably venomous spider?