I would start with zero but I think maybe he would start with one. The numbers one, two, three, four, and so on, and you think about which of those numbers are perfect squares. So zero squared is zero and one squared is one and two squared is four, three squared is nine, 16, 25, and so on. And Galileoobserved that, that the perfect squares can be put into a one-to-one correspondence with all of the numbers . I mean, we just did it. I associated every number
squares, perfect squares as there are numbers , and yet there's all the gaps in between the perfect squares, right? And, and this suggests that there should be fewer perfect squares, more numbers than squares because the numbers include all the squares plus a lot more in between them, right? And Galileo was quite troubled by this observation becausehe took it to cause a kind of incoherence in the comparison of infinite quantities, right? And another example is, if you take two line segments of different lengths,
- And prime factorization is every single number can be decomposed into the atoms of mathematics, which is the prime numbers . You can multiply them together to achieve that number.And that's prime factorization. You're showing 3 and 5 are both prime numbers , odd. So through this magical formula, you can deal with this
integers, which are discretely ordered, right? From any integer, there's a next one and a previous one, and so on. But that's not true in the rational numbers . And yet, the rational numbers are also still only a countable infinity. And the way to see that is actuallyit's just exactly the same as Hilbert's train again, because every fraction consists of two integers: the numerator and the denominator. And so if I tell you two natural
it's just exactly the same as Hilbert's train again, because every fraction consists of two integers: the numerator and the denominator. And so if I tell you two natural numbers , then you know what fraction I'm talking about. I mean, plus the sign issue, I mean if it's positive or negative. But if you just think about thepositive fractions, then, you know, you have the numbers of the form P over Q, where Q is not zero. So you can still do
- Okay, so Cantor wants to prove that the infinity of the real numbers is different and strictly larger than the infinity of the natural numbers . So the natural numbers are the numbers that start with zero and add one successively, so zero, one, two, three, and so on. And the real numbers , aswe said, are the numbers that come from the number line, including all the integers and the rationals and the algebraic numbers and
everybody, continues to have the ability to engage in strikes against Israel. numbers of missile strikes into the north of Israel where Israeli citizens live. There was a period of time after
charities that this will if not maybe charities that this will if not maybe not end rough sleeping but bring the not end rough sleeping but bring the numbers down significantly. And to the numbers down significantly. And to the point that Alex was saying, I mean, Andy point that Alex was saying, I mean, AndyBurnham today was visiting a a homeless Burnham today was visiting a a homeless hostel in Newcastle, and he acknowledged hostel in Newcastle, and he acknowledged
these Palestinian families, to take them food. And very quickly you saw a large numbers of Israeli soldiers blocking uh these activists and completely stopping them and getting rid of them. You know,they they were firing rubber bullets, they were using tear gas. And they did manage to get rid of those people very,
Nothing. It's simply, a continuation, of our naming system. Numbers represent generations, while letters indicate different product segments.The B Series builds on that success of the A Series, by expanding into a new segment while maintaining...
So, I love tech videos. Like, I love watching them, but I also love making them clearly. And they also have lots of numbers and stats and specs and technical details that are important.They matter a lot, but they can also be hard to keep full track of. What a lot of people probably don't see as much is
Science lets us understand the ocean in this way, and the cultural, intuitive thing lets us understand it in this way. Numbers have to be important.
changes in brightness that we are now capable of measuring. So this particular star got fainter. You know, a few numbers in the fourth decimal place. The brightness went down by just this tiny little amount. That tells us we're dealing with a roughly Earth-sizedplanet. And it repeats it looks like every 10 units or so. And when you look at what
There's a little subtlety in this equation because if you look closely, the F and the a have arrow signs on top of them, indicating they're not just numbers , but vectors. They have both a magnitude and a direction.So if you imagine writing those vectors as components in the x direction, y direction, z direction, then each component obeys F in the x direction
Harvick Right now, he's won nine races and we have. I think we're on nine of 30. You just, you know the numbers there. It's like, terrible. Then you fast forward Thio, the Lakers and the Heat. I don't know the exact record right now, but I'm sure it's more wins thanlosses on DSO ITT's levels. That and and so you have to look at okay, I have to be able to accept defeat. But
And that was something that only then I connected this to this very traditional movement, where they've now managed to attract higher numbers at these European festivals, with people coming from Poland, coming from other countries in Europe to join this neo-Nazi festivalin Germany. So also in this case, I do think that we're seeing new developments, where online platforms and tech
Do they travel hundreds of kilometers? numbers . It's really about trying to promote the resilience of communities, because, in the end, there is a lot of these emerging threats that are coming,
And as I started to look into the waste component of that, I was just startled by the numbers that I was reading, numbers like 40% of food never gets eaten.Around 20% of the water in this country goes to grow food that never gets eaten-- and similar numbers around energy,
A broad rise in crime through to somewhere around the late '80s, early '90s, and then a drop, and what Numbers increased dramatically, much more in New York City than in other American cities.
OK. He didn't go over it. Numbers ? What if I marked these squares with numbers ?
Numbers about the supposed consumers of video games have always been published, always been kind of contradicting themselves.
numbers went through the roof and through the device of reporting on what was on the moon the Sun became the most
numbers came out I'm G just be honest I just so I have to I want to be honest so
numbers absolutely beyond the grasp of the
Numbers change. You know, long time ago, $40,000 was lot of money.
Numbers were her friends.
Numbers chased each other around and around in Ada's head." And there she is with Mrs. Puff keeping her company through that long, hard time of her life.
Numbers themselves are very helpful and important, but we have to think about the decision rules and rules of engagement on our teams as well.
numbers might drop if there was a swine flu epidemic.
numbers over, then it means also you've got to reprogram the lights and all that stuff.
numbers of galaxies, are clearly intimately tied to the evolution of galaxies and super massive black holes.
numbers to make their case case. And these distortions can have a significant effect on our world. Here's just one example, uh, one that I find
numbers and less about what's the long-term value. And so, those decisions get truncated
numbers in any way at all is all good.
numbers that we like to round up to because it makes anatomical sense. But why three?
numbers they were and when it was the zero tapped first, when it was tapped second. And where was zero?
numbers will become very important so I'm going to talk about the upper Airway resistance syndrome first
numbers of the planes flying.
numbers . But as you go further east, they turn into letters. The higher the letter in this case, the worse the neighborhood; the worst the block.
numbers of women moving up into those leadership positions. And because I have the experience as a woman who, women of my generation who've really
numbers , absolutely pathetic. And all four units with the Christmas season coming on, no less. Depressing people; drooling like bilge down the plate glass window at the Cactus
numbers , or multiplying fractions, or whatever. And so that was -- the premise was, "I'll give you as many problems as you need until you get ten in a row" and I'll show you what
numbers and his desire to die in battle these things I've never understood in
numbers he ever took, pretty much all his life, essentially, spelled out there. So, now you parti-, perhaps can understand why it's interesting for us because he's a person
numbers or prosperity to becoming a species that totally dominates the planet. Because if you look at a graph of human brain size over time--from fossils--like this one, you
numbers let us know. Let me know.
numbers of science and engineering PhD's. You know, an example of this kind of anxiety came during the last presidential campaign, when President Obama at one of his campaign
numbers drop off drastically now I also want to point something out and this may come as a
numbers carbon trajectory if you did if you used a
numbers and of course he's the right guy to to be of use for that um