Content deleted Content added
Line 507:
:: Probably, the article could better go into some detail on why and for what the diagonal argument being applied to natural and real numbers is important in mathematics as well as in the "real world", so that a lay reader like me could really understand there is no life without this argument in this or that important field of human activity or imagination. A layman's view is that generic real numbers correspond to nothing in the world we see and experince, and in this sense do not exist, that they are only idealizations of our real and always finite knowledge, and that infinite lists of numbers (be they real or natural) do not exist in the same way, so any layman and not only me is naturally interested why mathematicians study different kinds of non-existence. [[Special:Contributions/91.122.7.114|91.122.7.114]] ([[User talk:91.122.7.114|talk]]) 00:51, 19 January 2013 (UTC)
::: Forget all that philosophy, what bothers me for real is this: how can one say he has picked ''all'' the natural numbers? One gave me a bucket of numbers and said: "That's all, there are no more natural numbers". I determined what number is the maximal one in the bucket (if that guy was able to pick them all, then I can inspect them all; and if the guy is not able to pick them all, then no infinite list can be built anyway) and then named a number that is greater by one, so that to add it into the bucket. Then I said, "Now all the natural numbers are in the bucket", and gave the bucket back to my friend, but he disagreed, on the same grounds. Something here must be wrong, but what exactly? - [[Special:Contributions/91.122.7.114|91.122.7.114]] ([[User talk:91.122.7.114|talk]]) 05:27, 19 January 2013 (UTC)
:::: Well, seems like the beaut is that the work is never done but the features of its state are the same at whatever point. I can imagine Cantor's devil as a machine that, first, declares it's going to do something abominable (names what and why), reserves ''B-1'' infinite-length registers (''B'' being the base of the numeral system to use), initializes the registers with empty sequences, and then proceeds: at each step, it picks a natural number, generates an (infinite: ???) sequence of digits, seeks a digit on the position that corresponds to the number just picked, makes a set of other digits, and for each of them, adds the digit to a sequence in a reserved register. Of course, it never finishes its work, but whatever the finish can be, we'll see that when it has come, there are only so much natural numbers, but the sequences of digits outnumber them anyway (whatever nonsense those sequences are).
:::: The problem (my problem and all the readers') is that the finish can't be (from the habitual point of view), and thinking of it is meaningless, unless there is such and such reason to accept this way of thinking in this exactly situation. The rest is to understand what are the reasons to accept these things, and I think this is what the article fails to demonstrate, and that's why so many questions from us all. I guess it might be improved in this direction: i.e., show context.
==Cantor's Nonsense: Pseudo-mathematics at its best.==
| |||