Posts by Michael Homer
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All of which was a bit handwavy, but the gist of it is that yes, there is more than one infinity, and they are meaningfully different in some situations. Not cheating; the distinction between countably infinite and uncountably infinite really is important.
The rest of the infinities are less practical.
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Different kinds of infinity:
From memory (I think of a PHIL paper, though it could have been maths), it's things like:
{1, 2, 3, 4, 5 ... } is smaller than
{2, 4, 6, 8, 10 ... }You can add them together and stuff.
No. {1, 2, 3, ...} is smaller than the reals (i.e. decimal numbers), but the same size as {2, 4, 6, ...} or any other infinite subset of the integers.
For that case in particular, clearly {2, 4, 6, ...} is included in {1, 2, 3, 4, 5, 6, ...}, so it can't be bigger. You can transform one into the other by doubling or halving every element, so they must be the same size. That infinity is called aleph-zero.
The real numbers are uncountable, meaning they can't be matched one-to-one with the natural numbers 1, 2, 3, .... Their infinity is called 2^(aleph-zero), and it's distinct from aleph-zero itself. It may or may not be the same as aleph-one.
Virtually any infinity you might encounter outside of mathematical theory is the same size as one or other of those. There are infinitely many other infinities you can reach by transforming those, and also some others that are qualitatively different and less common. Outside of mathematics it doesn't really matter which one you have though.
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Please do fix the RSS feed, though. I would read more posts if they were there, rather than blowing it off when the couple of lines' teaser isn't immediately enticing. Often they're pretty useless; especially given how meandering the posts can be.
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Well, for one thing, you don't know if a vid contains infringing material until after you've seen ("downloaded") it. The same argument doesn't quite hold for torrents, etc.
Why not? You can't possibly know what's in anything until you've downloaded it already, by which time you've already infringed. There's no difference between downloading from Youtube and downloading anything else that I can see.
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[...] if a Governor-General was dismissed, then the role would revert temporarily to the Administrator, whom the PM and the Queen cannot dismiss.
It might only take a few days (or hours), but while the new Governor-General is in the process of being appointed, I'd like to think the Chief Justice would do something if the situation warranted it (perhaps dissolving Parliament [...]
What is the process? Is there necessarily a gap between the two, or can a new appointment be an instantaneous replacement? Sending "Liz: please appoint me GG" seems like it would be sufficient, and nobody else would need find out until after the fact. All assuming the sovereign doesn't willfully obstruct things, of course.