On Jun 17, 10:30 pm, Tim Little <t...@little-possums.net> wrote: > On 2010-06-18, Ross A. Finlayson <ross.finlay...@gmail.com> wrote: > > > The rationals are well known to be countable, and things aren't both > > countable and uncountable, so to have a reason to think that > > arguments about the real numbers that are used to establish that > > they are uncountable apply also to the rationals, the integer > > fractions, has for an example in Cantor's first argument, about the > > nested intervals, that the rationals are dense in the reals, so even > > though they aren't gapless or complete, they are no- where > > non-dense, they are everywhere dense on the real number line. > > As your sentence is less than coherent, I will merely point out that > it is generally poor form to use 9 commas in a single sentence except > when listing items. I will grant that parody often benefits from > abuses of ordinary sentence structure, such as, for example, and not > in any way showing that these are the only possible forms, sentences, > like this one, which are convoluted to exhibit, by way of meandering, > that they imply that mental processes, of the original writer, that > is, which may be, perhaps, less than clear, and so in some way, to > some readers, humourous. > > - Tim
Some I go back and add later.
Too bad no one can read it but me.
No seriously still it's clear in lots of ways, I can rewrite those paragraphs as much longer.
Sorry that was a bad joke. Collected, I'm very happy with the output. Each one, in its own way, has some content.
You don't agree with the rationals are dense on the line?
The rationals are well known to be countable, and things aren't both countable and uncountable, so to have a reason to think that arguments about the real numbers that are used to establish that they are uncountable apply also to the rationals, the integer fractions, has for an example in Cantor's first argument, about the nested intervals, that the rationals are dense in the reals, so even though they aren't gapless or complete, they are no- where non-dense, they are everywhere dense on the real number line.
The rationals are well known to be countable, and things aren't both countable and uncountable, so to have a reason to think that arguments about the real numbers that are used to establish that they are uncountable apply also to the rationals, the integer fractions, has for an example in Cantor's first argument, about the nested intervals, that the rationals are dense in the reals, so even though they aren't gapless or complete, they are no- where non-dense, they are everywhere dense on the real number line.
(The rationals are well known to be countable, and things aren't both countable and uncountable, so ) to have a reason to think that arguments about the real numbers that are used to establish that they are uncountable apply also to the rationals, the integer fractions, has for an example in Cantor's first argument, about the nested intervals, that the rationals are dense in the reals, so even though they aren't gapless or complete, they are no- where non-dense, they are everywhere dense on the real number line. (...)
You left out the part before and after.
Arguments about the uncountability of the real numbers include those derived from the numeric property of their density. For example one of them is called "Cantor's first argument for the uncountability of the reals."
The constructive (computable) sets are mappable to the countable ordinals, where, the countable ordinals is the same thing as the enumerative ordinals, because, they're each countable and that's all of them. The constructive universe is complete, each in it countable, but then the results of results are results so they are infinite and their own powersets. (Sound familiar?) The existence of the constructive universe is a result.
Ha what's funny is you can still read them.
Basically from having an idea to write a sentence, as it's written then the parts of it are added automatically for, as you describe, contemplative pause, as well as any emplacement of comment to provide context generally. This is in the case where the writing is for a particular medium, when there's a lot of writing back in forth (in complete sentences, thank you) then to edit for readability is deferred for real intent. But, there's not really a lot of writing going on that way, rather, I much prefer the writing with the theme and the content (on the mathematics). So, I read.
