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ALG Mini MA912D71 Form A 1 U is the set of natural numbers less than 8. G is the set of even integers less than 10. Which is the complement of set G in universe U? A. B. C. D. 2 Let A, b, d, f, g

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I'm going to give you an astounding result Astounding? An astounding result So I'm just going to write down a little sum I'm just going to see what answer it gives. 1 + 2 + 3 + 4 + duh duh duh duh duh And I include all the natural numbers, so all the way up to infinity So what do you reckon the answer to this is, Brady? —Well I would say it would go to tend towards infinity. Yeah, that makes sense, doesn't it. The answer to this sum is -- remarkably -- minus a twelfth. It's amazing! I mean, I first saw this result when I start learning a bit of String Theory And what's even more bizarre is that this result is used in many areas of physics This is a very well known string theory textbook by Joe Polanski. As you can see, sort of quite early on, page 22, we have this statement here which is that the sum of all this is --- basically saying the sum of all the integers --- all natural numbers all the way up to infinity, is, minus a twelfth. Alright so we're going to prove now, Without getting our knickers in a twist with Riemann zeta functions, we're going to prove in quite simple way, why the sum of all the natural numbers is indeed minus a twelfth. So, to do that we're going to do this in a number of steps. We're gonna to look at a few different sums. The first sum that I want to look at, I'm going to call it S1. And it's 1 -1 +1 -1 +1 -1 and so on. That's the first sum I want to look at in principle. The second sum I'm gonna look at is 1-2+3-4 and so on Carry on in that process all the way up. And the third one is of course going to be the one we're really interested in which is 1+2+3+4... and so on. So we're going to evaluate all these 3 different sums. Now the first one is really easy to evaluate. We need to attach a number. Now clearly what is the answer to this? You stop this at any point. Okay, if you stop it at an odd point you're going to get the answer 1. You stop it at an even point you'll get the answer 0, clearly. That's obvious right? So what number are we going to attach to this infinite sum? Do we stop at an odd or an even point? We don't know, so we take the average of the two. So the answer is a half. There are other ways to prove that this sum is a half by the way, which we can do if you want... No, no, there'll be a link, there'll be a link there, 'cause we've done it before. Ok, good ... See the link there Ok, so this is a half and I think intuitively that's the easiest way to say that you either get 0 or 1, and therefore you just take the average... So this is the natural number to attach to this sum. So once we know this we're laughing, ok? Because from this we can achieve everything we want to achieve. The next step is to find out what this sum is. So what I'm going to do is... I'm going to take two copies of this S2, ok. So I'm going to add it to itself. So 2 times S2 is equal to... Let me just write it out. I will write it out twice 1 -2 +3 -4 duh duh duh and so on. And then I'm going to add to it itself, but I'm going to...

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What is u is form set?

The u is form set refers to a set of forms, including Form U and Form IS, that are used for reporting certain financial and investment information.

Who is required to file u is form set?

Individuals and entities that meet certain criteria, such as being a registered investment advisor or having a certain amount of assets under management, may be required to file the u is form set.

How to fill out u is form set?

The u is form set is typically filled out by providing the requested financial and investment information on the applicable forms. It is recommended to consult the official instructions provided by the relevant regulatory authority for detailed guidance on how to fill out the forms correctly.

What is the purpose of u is form set?

The purpose of the u is form set is to collect and report financial and investment information in order to fulfill regulatory and compliance requirements, monitor investment activities, and ensure transparency in the financial industry.

What information must be reported on u is form set?

The specific information that must be reported on the u is form set may vary depending on the applicable regulations and reporting requirements. Generally, it may include details about assets under management, investment strategies, fees charged, and any disclosures or disclosures required by the regulatory authority.