Listen to native speakers pronounce “uncountable” in real conversational contexts with synchronized timestamps and subtitles.
But all those things are good.Uncountable. So yeah, that's really the answer.
The people spoke 6,500 different languages, representing tens of thousands of different cultures producedby uncountable different histories.And yet, on that day, they all began to attend to the very same unlikely thing, the three American men with lunch bucket names like Frank and Jim
is trying to manipulate the game industry.It generated thousands uncountable number of memes and ongoing online conversations, and, of course,not everyone who has been accused by the Gamergate campaign was a woman, and most of them were, in fact, women.
It just said one must exist, but can something exist if we can't actually build it?His proof also used an uncountable number of steps, was that even allowed?Some mathematicians argued proofs should be finite, others accepted infinity, but only the countable kind and then things got worse.
Even for infinite sets, it's easy if there's a clear rule, like always choose the smallest thing, but sometimes there is no natural rule.In those cases when you're choosing from infinitely many sets, including the uncountable ones, you need the axiom of choice.We can't say how we're choosing, but the axiom makes all of these choices all at once.
- Yeah, it's a really nice visual way to think about it. You just zigzag your way across the grid to make sure everybody's included. That gives you an algorithm for includingeverybody. So, can you speak to the uncountable infinities?- Yeah, absolutely. - What are the integers and the real numbers- - Correct - and what is the line that Cantor was able to find?
choice is being used and they don't want to use the axiom of choice, so they work out the consequences that's- that are possible without the axiom of choice or with weakenedway. Even though the contents of those statements might be referring to infinite uncountable objects,
That was similarly being seen as another elite that was trying to control game culture.In my research at the time, I'd been reading an uncountable number of threads and comments left on Reddit, on Twitter, and so on around Gamergate,and one of them, at some point, really caught my attention.
You can literally count them, one, two, three and so on.So Cantor called these countable infinities, but then there are bigger infinities, Cantor called them uncountable.These infinities like the set of all real numbers, the complex numbers, they can't be matched one-to-one with the natural numbers.
but formulates explicitly nowhere.See, all along, Cantor had been assuming that he could make an infinite number of choices at once from any set, including uncountable infinite sets like the real numbers,but this was just an assumption.
in a way that was so compelling. He exhibited two different infinite sets and proved that they're not equinumerous; they can't be put into one-to-onecorrespondence. It's traditional to talk about the uncountability of the real numbers. Cantor's big result was that the set of all real numbers is an uncountable set. Maybe if we'regoing to talk about countable sets, then I would suggest that we talk about Hilbert's Hotel, which really makes that idea perfectly clear.
choice is being used and they don't want to use the axiom of choice, so they work out the consequences that's- that are possible without the axiom of choice or with weakened- Right. So we talked about Cantor's proof that the real numbers, the set of real numbers is an uncountable infinity,
We're not really ever a literal kind of closed circle of game culture that you're either in or you're out.When you're mentoring about the people not using wearable gadgets and self-tracking, of course, there are uncountable reasons, which I have no idea
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