The following is a presentation of TFNN. Trade what you see with Larry Pezzavento. Call now toll free at 1-877-927-6648 or internationally at<PHONE_NUMBER>. Now, Larry Pezzavento. OK, folks, we're going to start out the show here. Paula Webb will be our guest here at the break. Tomorrow we're going to have a Grace Morris of Astro Economics. She'll be talking to us, of course, about Nvidia's earnings, which will come out today. And then on Friday, we have the wizard himself from Naples, Florida, Norm Winsky. So we've got two astrological people, two days in a row. Here is the Treasury bond, folks. We are completing a pattern known as the lightning bolt. It was also called the ABCD pattern. I don't know if you folks know this or not. But when Gardily wrote the book in 1937, he had four or five people copy parts of that book. The one that was most famous was a man named Franklin Tubbs. 1951 he came out with the I forget what he called it. You know, I'll have to remember, but he charged two thousand dollars for it, which was more than Gardily charged for his book, which was fifteen hundred dollars in 1937. And it was basically the A.B. Equal CD pattern, the Franklin Tubbs. It was an ABCD. Charles Lindsay came out in 74 and called it P1, P2, P3, P4. Exactly the same thing. They were doing exactly the same thing. So I'm doing the same stuff. Many people have done, but it works for me. You know, it doesn't work all the time, but it works some of the time, and that's all you really need to do. So here's what we're watching here in the box. Now, we've made new lows now with the last six days, but it hasn't fallen out of bed yet. I'm not sure if the Fed is speaking now or not, but the low so far today was one seventeen twenty one. We're trading a one seventeen twenty four. Now, if you're interested in buying bonds, I don't know if the Fed's out there now, but if the Fed is out there, you still got to put your stop in here somewhere, you know. So if you want to risk ten ticks, twenty ticks, five well, five ticks is probably too small, but nothing less than ten ticks. This is the place where you take your shot. That's basically, you know, what you're looking at. I know a lot of folks here get tired of here in ABC all the time. But folks, the only reason I say it because it works a lot of the time. I've never found anything else that works as well as this. Look at this on just on a little bit daily right here. There's your ABC D leg right there. Now here you see it went quite a bit above it. It was supposed to come in at one twenty four twenty. And it came in at one twenty five thirty. It went a whole point. But finally before it went over and then on the way down, you'll see here it is again. There's your ABC D right there. And this one came in spot on exactly within two ticks and rallied up. And so here's where we are right now. I just bought them and I bought them twenty five. I'm going to stop at ten. So I'm going to have 15 ticks and I'll tighten that up. If it starts making lower lows, I don't know if the feds out there. Not because I really don't. I really don't follow them too much. And you know what, folks, they don't follow me too much either. So we're pretty much tied. OK, now let's move on to something else that the several people have been asking me about. And that is the stock market. And let's get up here for one second here. See, here's where we were. We're going to go back here just for kicks and giggles. All right, because market has come down very, very quietly. Here's where we were Sunday night. OK, there was a three eight two right there. That was the one from Sunday night when we were on vacation and getting ready for the holiday. There it was right there. Hit right on the money at. Well, it missed it by half a tick. But well, actually, yeah, it did twenty nine fifty. And fifty twenty nine fifty. The high was fifty twenty nine fifty. So it missed it by half a point and that's pretty close. So we were we were using the Dow Jones, which made it. So that was OK. You were still short that. Now we're coming down, but it's very quiet. Look, three, four days down, very, very quiet. This market's not falling out of bed for any reason. So if we look at this on a hourly chart, just get it up here. You'll see it's just coming down to where we're almost at the seventy eight percent level right in here. There there is your seventy eight. We made a lower load just a second ago right in here. Didn't go anywhere. So this is acting pretty nicely. So watch for watch for another retracement. What I'll be watching for today, if the Fed does anything crazy, is to go up and just to see if there's going to be some type of a three eight two rally in here somewhere. You'll see it that would come in here at fifty twenty. That's a three eight two off the high. So that that'll be a big one. That'd be up twenty five handles, folks. You think they're not going to be some people that were short in here. It's not going to get scared up in here. Well, of course they will. So that's why you've got to be you've got to be super careful doing it. The ABCDs, they work. I keep saying this. They work about sixty percent of the time, folks. And the other forty percent that you're going to you're going to law. You're going to lose. And all you have to do is try to handle your losses. And you should be you should be handling it. OK, that's the way I'm looking at. We've got a we've got a couple of positions on now. We've we bought wheat today. Well, I'll just re reiterate it because the wheat made a three eight two retracement. We were this was really I missed this one right there. You see it hit it exactly right there. So we bought the wheat there. Our stop now is one tick below here. So we're risking basically basically less than fifty dollars in that. But look at this, folks, on the daily chart. This was a that's not the one I want to want. Four hour. That's what I want to watch. There is the four hour chart. Look at it right here. This is going back over since December. The number came in at five fifty two. The low was five fifty five fifty two. You can see five fifty three was one point two seven expansion right in here.  All it's done is just back off to the three eight two so far might be a little early. But you know, we've got a full moon coming in tomorrow. And the next day and the next day, both Thursday and Friday, we'll all be part of it because it takes three days for that full moon to you know, go through its little dance that it does every every 14 days from full moon to new moon. And we'll see what happens there. Now, all I do with the full moon, I just count the days, folks. I'm not interested in whether it's a lunar thing or whether the moon is in Scorpio or any that kind of stuff. I just look at the counts and I count them to see if I can get something that tells me there's some symmetry there. That's really all I'm trying to do when I do this. It's it's kept me in the game for a long time. And I hope it'll keep me in the game, you know, a lot longer. So those are some of the things that I'm watching. Now, just to show you today, the value of the three eight two. Here is the Dow Jones. OK, now here was the high that we made here on Friday. You see today's high wasn't we made a low. And then we rallied up and made the high right up in here. And then we've come down. So I'm watching to see if it gets back up to this level. One more. This is still made a three eight two. It came within five pips of the exact three eight two from that level. Then it broke all the way down and has been bouncing around all morning. So that's what we're that's what we're watching today with these markets. But none is more important than the Treasury bonds. And the reason for that is, folks, that's the biggest market of them all. And that's the one that you want to pay very, very close attention to. OK, now, quick, quick view of the soybeans here. We were trying to buy the soybeans today at forty eight. And we did. The number was forty seven. We bought it at forty eight. It had a little bit of a rally here. And I saw that rally in the first thing I did. Let's just go back and look to see if there's trouble in paradise. And there it was right there, folks, almost exactly at the three eight two. So this market's not stopped going down, but it's getting close, in my opinion. But remember, opinions are like armpits. Everybody has one in it usually is a little smelly. Let's move on. Take a break here. Pay a few bills for TFNN and we'll be right back. Eight seven seven nine two seven six six four eight. Steve Rhodes started his trading career as a student almost 20 years ago. And the student has now become the master. Steve won the prestigious Timer of the Year Award in 2018 and barely missed that mark again in 2019, finishing at number two for the year. An amazing accomplishment. Steve Rhodes is committed to sharing his techniques and knowledge with anyone who wants to learn, and he shares his vast amount of trading knowledge every day in his Mastering Probability Newsletter. Steve's award-winning newsletter, Mastering Probability, is delivered every trading day with updates throughout the afternoon. Sign up for Steve's market newsletter, Mastering Probability, and you'll receive access to seven of Steve's educational webinars absolutely free at TFNN. All our newsletters come with a 30-day money-back guarantee, so you have absolutely nothing to worry about. Visit TFNN.com and try Mastering Probability 30 days risk-free today. TFNN Educating Investors. Are you ready to take your trading to the next level? Introducing Tom O'Brien's award-winning newsletter, Market Insights, your key to successful active trading. Tom O'Brien, renowned for his expertise in the financial markets, has designed Market Insights to be your daily guide to profitable trades. Tom publishes his daily Market Insights newsletter every market day before the market open, along with updates when warranted. Stay ahead of the game with Tom's real-time analysis and trade recommendations delivered straight to your inbox.  Ready to join the ranks of successful traders? Head over to TFNN.com and subscribe to Market Insights today. Don't miss out on this opportunity to supercharge your trading results. Market Insights comes with a 30-day money-back guarantee for all new subscribers, so you have nothing to risk. Don't miss out on this opportunity to revolutionize your trading game. Head over to TFNN.com right now to join thousands of traders who have already experienced the power of Tom O'Brien's award-winning newsletter, Market Insights firsthand. TFNN, educating investors. Are you ready to take charge of your financial future? TFNN is your gateway to the world of trading and investing. Whether you're starting out or scaling up, TFNN empowers traders and investors of all skill levels with top-notch investing systems, strategies, and techniques. It's time to protect and grow your money with insight you can trust. Join us live Monday through Friday during market hours for exclusive content that moves with the markets. At TFNN, we bring the trading floor to you. Our seasoned hosts are here to answer your calls and questions live on the air. Check out the Tiger's Den for just $1 and follow us on YouTube and become part of our vibrant community. And remember, at TFNN, we're so confident in the value we provide that we are for a 30-day money-back guarantee on all new premium newsletter subscriptions and services. You have absolutely nothing to risk. So why wait? Tune in live to Tiger TV and transform your trading journey because when you know better, you invest better. Join us and experience the difference today. TFNN, educating investors. OK, folks, you can see here, this is the Bible that I live by. This is 20 pages of my notes that I took with Mark Douglas here for six years from 96 to 03, actually almost seven years. And it was a revelation to me. I've known him for so long and we were very close. He was the best man at my wedding and Paula married us, of course. And we traveled the world lecturing and over the years, or Mumbai and golly gee, just so many places. Anyway, miss him. I miss 20 minutes, great deal. But they're still in my heart because I when I see this book here, I can see Mark sitting next to me, you know, drilling these things into me and believe me, folks, being a hard-headed Italian like I am, it was not easy for him. But we made fun of the situation. We got it done, took a long time. But it was I mean, I was doing good. I mean, I was not the problem was I thought I knew more than I did. I knew a lot about the markets, but I didn't know about the most important cycle, which was the left ear to the right ear. So I'm going to take a few minutes here because I know some of you folks, you look at the patterns and you think that they're important. They are, in some respect, because it's a trigger mechanism. But the mechanism that means the most is the mechanism. It's between that, that 90 between this year and that year, that nine inch cycle. And that's the one you've got to get right. Once you get that right, you know, you've got it made. People ask me all the time, well, how do I know whether I can afford to take the risk? Well, if you can, it's simple, it's a dollar amount. Can you afford to take a risk of six hundred dollars? If the answer is yes, then you've got to take the trade. If it's a completed pattern, you've got to do it. Now, you'll notice right here, here's one that I'm looking for, whether it happens or not. I don't know, but we're in an oversold market. And I think we've got a possibility of making this 61 percent retracement here, especially if the Fed's out here doing something. So I'll be looking to be a seller here with my stop above here.  Let me just quickly do this right here, because there was your first ABC. Now, I'm not, I'm not watching the NASDAQ today. I'm not watching the S&P. I'm just watching and look at the low. I mean, is that hard to figure that out? There was a low 30, 40, 50. All right. What we do, we rallied up to the 382. Then we backed off and this is what we're doing. We're backing and filling right now. So that's what my game plan happens to be. But that doesn't mean anything. This is what means something, folks. This little thing right here, because let me just go through some of these things. In order to be successful as this, you have to have a foundation of absolute trust in the patterns and the ratios that you're dealing with. Number one, number two, you have to have a pattern of trust for protecting your big, you know what, your big kahuna that you set on all the time. Because if you're not out there protecting yourself, folks, you might as well go over to McDonald's and start flipping burgers because it's just a matter of time for the hand you your lunch. Might not be today, might not be tomorrow, might not be for three weeks, three months, three years.  That's the only protection you have is the stop-law orders that is out there. What would the Fed would come out here today? And let's say in about 20 minutes that, well, the economy is actually, these figures are not really as strong as they should be. So we're going to start cutting interest rates right now. What do you think would happen to the stock market and the bond market? Well, you're right. They'd probably have one heck of a rally. Maybe not. I don't know. But I'm saying that's the risk that you have to take if you're out there doing that. So you've got to remember to do that. You have to formulate these rules for yourself with a hesitation. Number one is you ask yourself, this was this was right out of Amos Hostetter. If you can afford to take the risk, OK, that's number one. And if you are sure that you're protected, that's number two. You must take the trade because one particular reason that we all know no one knows what's going to happen next. And I mean no one. So if you can answer both those questions, yes, I can afford to take the risk and I can protect myself. Then you can put this you can put the trade on. I get at least one email a day. How much should I risk if I'm going to do something? I can't tell someone how much they're going to risk. I don't know what their bank account could be. Two million, twenty million, you know, three hundred dollars. I don't know. You have to find out what that risk factor is. Now, everything that we trade here is based on usually a maximum with like crude oil. And and now the S&P crude oil, gold and the S&P are having a risk factor of about a thousand bucks, somewhere between eight hundred and a thousand dollars. That'll cover almost anything. But look how nicely that ABCD worked today in the Dow Jones. It went right down to the bottom and flat stopped right there.  So this was yesterday's high, interday high, boom, there it is. So nothing more than that. So all I'm doing is reversing the process, seeing what's going to go up here. So I asked myself the question, can I afford to take the risk? Yes. Am I protected against that risk? Yes. Then I have to take the trade. The reason why is I don't know which one's going to work. And you know what, I don't really care. That's that's the bottom line. I just really don't because I just keep doing them and I keep doing them and I keep doing them. Sometimes they work, sometimes they work. But overall, it's going to get you to the promised land. Yeah, you're going to have times where you lose five, six, seven. The heck as many as 11 times, 12 times. But boy, when you're on fire, you think gets it all back very quickly. By the way, those four and five times in a row, those are outlier events. You don't see those very often. So you got to remember, if it's a valid signal and you know how much you're going to risk, then you have to put the trade on because you don't know what's going to happen next. And that'll, what that will do if you do that, it'll develop to the consistency that you need to put all the trades on, not just the ones you think are the best folks. The ones that I think are the best are the ones that hardly ever worked for me. You guys been following me for a long time and you know when I'm really, really excited about something, you know, my goodness, you'll be more careful about that than anything because those are the ones that scare me. Look at this, there's no way this one cannot work and what boom, it didn't work. So that's why you got to get used to doing that. You know, I used to sit here, listening to Mark talking to some of these guys that paid him a lot of money. And these guys were really famous. Their names are household worlds in our, words in our business, names in our business and they had the same things going on in their mind. You know, why do I know what's going to happen next? And they all ask the same thing. And once, you know, Mark would sit there and spend one or two days just explaining to him, you don't know what's going to happen next. No one knows the future, no one, except God and she quit trading a long time ago. She didn't need the money. Anyway, that's what, that's what this is all about is to try to find the ones that line up the best. But this whole book here, it's a 30-some pages of all the things that everything, and of course the number one thing on this big page right here, it says money management always takes precedent over technicals. No question about that. I know you've heard the story about the guy who was in the Maryland office that day. He was a big gang guy and he said, there is no way that soybeans are going to go, you know, a penny below. I think it was 525, 625. I don't remember the number, but it was, let's say it was 825. And the guy picked up the phone. It was Jack Waldock at the very lens, a partner and he picked up the phone and he said, he said, sell me 20 July beans at the market and they dropped seven cents. It was late in the day, markets were thin and the guy walked out of the office disillusioned. He ended up teaching gang for many years, but that was one instance where he said they could never go below there. And one trader with the deep pockets and 20 contracts for beans back in those days was a lot.  Hey, let's take a break here. We're going to have Paula T. Webb coming on the phone here in just a second. So we'll be right back. The gold report. As a precious metal, gold is still king. It continues to hold the most effective safe haven and hedging properties across the global major trading hubs of the London OTC market, the US futures market and the Shanghai gold exchange. The gold report. Tom O'Brien publishes his weekly gold report every Monday morning for subscribers consisting of coverage of the XAU, HUI, GDX, the dollar, bonds, the South African Rand as well as 25 different mining equities with specific buy-sell recommendations. The gold report. New subscribers get a 30-day money back guarantee so you have nothing to risk. Subscribe to Tom O'Brien's gold report newsletter now at TFNN.com. Currencies, commodities and bond markets are as important as ever right now with how they're driving the volatility in equity markets across the globe, which is why it's a great time to try out Teddy Kegstad's Tiger Forex report. Teddy Kegstad breaks down the forex markets every Monday using his 30-plus years of experience as a trading veteran of futures, forex, stocks and options. Teddy releases his weekly Tiger Forex report every Monday morning with coverage of all the major currency pairs, including the dollar index, the euro dollar, pound dollar, dollar Swiss, dollar yen, as well as many more. And he also has weekly coverage of the crude oil market and the 30-year T-bonds as they both influence forex markets tremendously. When you sign up for the Tiger Forex report, you also gain instant access to Teddy's 60-minute webinar archive he just hosted, forex strategies and fundamentals, what is behind the Tiger Forex report. For all the details and to start your 30-day Tiger Forex report subscription today, visit the front page of TFNN.com. TFNN Educating Investors. Everything in the universe is governed by the Fibonacci sequence. This mathematical principle is responsible for everything from the most aesthetically pleasing artwork to patterns in the stock market. To stay on top of stock patterns that you can take advantage of, sign up for the Fibonacci 24-7 newsletter at TFNN.com. When you subscribe, you'll get a weekly report from Veteran Day Trader Larry Pesavento on stocks you need to pay attention to and you can trust Larry's analysis. After all, he's got 45 years experience as a day trader. Larry will also provide daily charts, videos and data on the key markets that he's tracking. Expect notifications from Larry on market movement you need to act on at any time. First-time subscribers also get a 30-day money back guarantee. If you're not satisfied, let us know and you'll get a full refund within 30 days of signing up. Subscribe to the Fibonacci 24-7 newsletter today. TFNN.com Educating Investors. Don't forget, you can listen to TFNN live on your mobile device 24 hours per day. Go to TFNN.com and hit watch Tiger TV. Folks, so we have Paula Webb, Tomasini Douglas. Did I do that right? Is it Tomasini Webb or Webb Tomasini? That's a family. Anything you call me is just fine, Larry. As long as it's not late for dinner, I understand. Which she happens to be one of the best cooks around. Paula T, one of the things that I have, you know, from when people drop me emails is that how do I know whether a trade is going to work or not? And I try to beat it into them just like Mark did. You're never going to know that. You know, that's the whole reason the trading is because you don't know what's going to happen. How do you handle that when people, you know, bring that question to you? Well, anybody who asks that obviously doesn't believe there's always opportunity in the market. Right? It makes good sense. So they're kind of like counting on that specific trade to be a winner. So, you know, that kind of has to go back to the basics of the trade. So, you know, that kind of has to go back to the basics of if you don't believe that there's always opportunity, then, you know, how can you see actual market data when you're looking at your chart and doing your analysis? You have to always believe that at any given moment, sorry, I got something in my eye. At any given moment, the market can provide you an opportunity to take profit. And you can't just hang it all on one trade. That's right.  You may not be following your rules because you don't believe in them. And so, you know, you tend to wish and hope instead of actually having an objective state of mind to achieve your trading goals. And it's pretty typical, especially not even just in new traders. I mean, even seasoned traders can fall into that, shall we say, closed loop again of wishing and hoping, especially in today's markets. Do you have any special exercises that when you work with someone that helps them get through that stuff? I know you do because I did it with you for many years too. That's a true question. Well, one of the things that I always ask traders who get stuck in this closed loop and other ones as well is, what kind of promises did you make to yourself the last time you hung your hat on one specific trade that went south?  You promised yourself you weren't going to do that again. Right? Yeah. We all do that. We all say, okay, God, you know, give me a winning trade and, you know, I'll follow my rules. I promise. And yet they don't. They don't follow through on their promises. So, you know, what I tell traders to do is they have to sit down and ask yourself why making a promise to yourself to learn how to take profit and keep it, why wouldn't you do that? Why wouldn't you follow through on that considering it's your money that you want to grow? It's your money that you worked for to open a trading account with. So why wouldn't you make that investment in yourself and follow through on that promise to follow your rules as only you know how? Right? Does that make sense? Absolutely, yep. Sounds like Mark's sitting right here with me once again. Yeah, I mean, you know, we didn't write the books together for no reason, but I should clarify that. The discipline trader is actually, for sure, Mark and I wrote that together. And finally, after all these years, the publisher is adding my name as co-author to the discipline trader. So that's, I just want to mention that because there's always confusion because my name isn't on the first two books, but it will be on the discipline trader. Trading in the zone, I didn't necessarily co-write with him. As you know, he sat in your home writing a lot of it, but I did the editing. And you know, as you know, he shared a lot of that material with both of us to see if we understood it first. So we were kind of like the test market for trading in the zone. It's really amazing to me, even after all these years, that trading is really so simple. You have a belief in what you're doing. You know how to protect your rear-end. You know how to put the order in. That's all there is to it.   Right. I'm sure people might, well, maybe not our younger viewers, but a lot of people might remember Ron Popiah, who had all those kitchen gadgets, and he had that rotisserie. Oh, yeah. Oh, yeah, the guy on TV, sure, yeah. Yeah, right. He made billions of dollars with his little quirky little phrases. Yeah, all that stuff, yeah. And for the tabletop rotisserie, which Mark and I had one of those, his mother gave us for Christmas present one year, that phrase was set it and forget it. And so that's what I tell traders, you know, set it and forget it. Put your trade on, put in your stop, and forget about it, you know. And now if you can't maintain consistency, that's a good way to get started to building consistency. Just set it, forget it, turn your computer off, go do something else, and come back the next day and wait for your next setup. People don't believe me when I tell them I'm not in front of the computer a lot during the day. I put my orders in, and then I do some other things.  And because we thought we were going to, you know, look at some a lot of different patterns at one time, it ended up he had his laptop and I had mine. They haven't been turned on for 15 years. They're brand new. Anybody wants them? Well, we know, too expensive to ship. But I just keep it as simple as I possibly can. And I tell people that, but they certainly have a hard time getting through it. But the mental part of this though, polity, when I look back at all the stuff and with Jimmy passing away, you know, recently, and he was talking about the, oh yeah, you know how close we were. But, you know, my goodness, whenever we were visiting, we would have trades on, but we'd never be watching the market. And you know what? I don't think the market really cared where we were watching or not. I guess they never told us that they cared. Yeah, markets don't take it personal when you're not watching them. Yeah, that's the understatement of the year. Anyway, do you have anything special that the folks could contact you to maybe find out something that would help them in their trading? Well, you know, I've got my workshops going every other month. The Power Trading workshops. And we've got one coming up the first weekend in March. And there's still room. We can do one-on-one workshops. Those are really popular, the one-on-ones. It's a two-day workshop. I've got a new book coming out, The Sagacious Trader, which talks further about promising to yourself to make an investment in yourself as a trader. That should be out in a couple, probably by June, but don't quote me on that, I'll bring it behind. But, you know, just go to my website, polityweb.com and, you know, the free call is always an option to just chat with me for 15 to 30 minutes see if what I provide is something you're looking for, what traders are looking for. And sometimes that's all you need. Lots of traders just need a little focus and I give it to them and that really brings me a lot of happiness because that's what it's all about is helping others. You know that, Larry. I've done a little of that in my past. Thanks to you guys for treating me to do that from years ago, even when we traveled to those distant lands like Mumbai. Of course, when we went to Mumbai, it was called Bombay. That's how long ago it's been. Hey, listen, thanks for joining us, sweetie, and we'll have you on again soon. By the way, Tim Slater says hello. Yeah, you know, give me, text me his number. Would you please, I want to get him on the line. He's the guy that started all these charts for left off. Yes, and we were talking. 40 years ago. That's right, 40 years ago. We'll get Tim on the line here. Is he still with Elaine? Yes. Send it to me, I'll call him. You might think that if you want to be successful at trading in the stock market, you're going to need a crystal ball. You're going to predict the future, right? Like any endeavor in life, before you decide it's impossible, get some advice from the experts. You might find that it's not so impossible after all. For daily market overviews that give you direction on the key indices, selective stocks, and commodities, subscribe to the opening call newsletter at tfnn.com. The opening call newsletter is written by Basil Chapman, creator of the trading methodology known as the Chapman Wave. The Chapman Wave up-down sequence gives you an edge in identifying price turns, finding the peaks and valleys in stock prices.  First-time subscribers also get a 30-day money-back guarantee. If you're not satisfied, let us know and you'll get a full refund within 30 days of signing up. tfnn.com Educating Investors Are you ready to take your trading to the next level? Introducing Tom O'Brien's award-winning newsletter, Market Insights, your key to successful active trading. Tom O'Brien, renowned for his expertise in the financial markets, has designed Market Insights to be your daily guide to profitable trades. Tom publishes his daily Market Insights newsletter every market day before the market open, along with updates when warranted. Stay ahead of the game with Tom's real-time analysis and trade recommendations delivered straight to your inbox.  For successful traders, head over to tfnn.com and subscribe to Market Insights today. Don't miss out on this opportunity to supercharge your trading results. Market Insights comes with a 30-day money-back guarantee for all new subscribers, so you have nothing to risk. Don't miss out on this opportunity to revolutionize your trading game. Head over to tfnn.com right now to join the thousands of traders who have already experienced the power of Tom O'Brien's award-winning newsletter, Market Insights firsthand. tfnn. Educating Investors Biotek is booming! But for how long? Whether you think the Biotek bull has room to run or has run its course, trade LABU or LABD. Directions daily S&P Biotek three times, bull and bear ETFs. Visit DirectionInvestments.com slash Biotek today. An investor should consider the investment objectives, risks, charges and expenses of the Direction shares carefully before investing. The Prospectus and Summary Prospectus contain this and other information about Direction shares. To obtain a Prospectus or Summary Prospectus please contact Direction shares at<PHONE_NUMBER>. The Prospectus or Summary Prospectus should be read carefully before investing. An investment in the funds is subject to risk including the possible loss of principle. The funds are designed to be utilized only by sophisticated investors such as traders and active investors. Distributor Four Side Fund Services, LLC This program is brought to you by Vista Gold. Traded on the NYSE American and TSX under the symbol VGZ. Okay, folks. I've got to put a chart up here of corn. This is a spot corn. Going back to 2020 you'll notice here that that's four years ago. We're down at the 78% level of that move right here. But folks just about every year you can see here April, May there's going to be some corn. You can see this is when you have your, here's your summertime rally. Okay, here's one in the spring. Here's another one in the spring. I mean, we always have rallies in these things. Now we're coming up here now. It's going to be rallying from a really different price level. But there's where we are going back. We had corn at 375 for many years, folks. Once it got to 475, they say, well, never see that again. And, of course, we went to eight and a quarter. This is the staple. This is the largest crop in our hemisphere, folks. And, of course, the South Americans do pretty good now. But this is the biggest crop. We're very, very low priced. We have the planning intentions is going to be coming out in about six weeks and the farmers are going to decide what they're going to plant. Now, look at this, folks. I mean, why is a farmer just like back in here, why would a farmer plant corn? This is what happened here. They didn't plant any corn. And boom, when they needed it, look what happened. It quadrupled in price. We went from $3 to almost $9 for heaven's sake. So this is what we're looking at. We want to find something like this, a really good opportunity. And I'm searching for it as we look at it. Now, what we'll do here, since we're looking at this, we're just going to blow this up just for kicks and giggles and see where we are on the ABCD front because we always like ABCD. Now, here was a 382 rally. Now, this is a weekly, okay? This is a weekly. So we see we had a nice move down. Now, I wonder what that went to. Let's just double check. We'll just mark. This is what we call the mother of all patterns, folks. When you get a 382 like this, oops, it's 50%. Let's see how close it is to 382 just for kicks and giggles. This thing is usually so accurate that it doesn't miss by much. Yup, there's a 382 right there. So it says 50%, but this is the actual one. You can see by this retracement right here, there's a 382. And then we come down and look where we are setting up right now somewhere in this ballpark. There's your AB leg. There's your CD leg right here. 414. The low so far has been 415. You can't get any closer than that, folks. We had a little bit of a bump here, but not very much. So what we're going to do now is we're going to look at this with the eyes of December corn because that's when you want to be watching. So we're going to come over here. Give me one second and get up to December corn. Here's December corn and we're going to put it up on the weekly and it'll be a little bit different, but we want to put this together so we can see it where we are going back here. You can see there's a difference in the crop months, but the lead month is the one we want to be looking at. So here's what we're going to do. We're going to look at this. We're going to look at the next move measure to 4747 473. Now we're 457. This is corn that has not been planted yet. So what we have to do is we have to look at the other ABCDs that are in this program. So we looked at the big one. Now we've got a couple of smaller ones in here, don't we? So that's the first one we're going to look at is this one right here. This is the ABCD 457, but we've got another one here too. We have to measure this ABCD from this one right here down to that one. You're going to see we start getting down closer. Now we're 465. We have one other thing to measure and that is the expansion of this weekly range from May through July. Remember July's when they have trouble with the crops and stuff and the 1.618 on that one comes in way down here at 436. So what this is telling me is December corn and remember December corn is selling for 17 cents more than the July corn that we're March or July corn that we're looking at right now. So they are already saying that they don't believe the farmers are going to be planning a lot or they are the farmers are going to be planning a lot and I think the farmers are going to surprise them. So I think we're at the point where you want to be ready to start buying corn. Now let's look at this on the daily. You'll see this is much weaker than the other. You can see we've well we just made another ABC down in here but the March corn has held up above this. So this is what's at 457 for December unplanned corn. If we look at the March corn come over here and take a look at that again one more time that would be right there and it is selling for 424. So there's 30 cent difference between the two. Okay so that's where we've got to pay where we're going to play the game and I think this is where the week or so maybe today, maybe tomorrow maybe during this lunar cycle that we have now that's going to be stretching through but boy certainly next week we've really got to look for a reversal sometime to get along the corn. We're already long beans we're already long wheat and we have our stops in so far you know they're hanging in there okay we got a well we got a 4 cent loss in corn in beans and we have a 4 cent profit a 5 cent profit in wheat so basically kits for the day so still have our stops in but these are the things that I'm looking at on the longer term basis because I think that the fact that this hit that exact number means a lot to me and then it rallied. Let's see it didn't rally much but let's see where it did rally too you'll see it rallied a little more than you might think it even gapped up oh this is the rollover folks this is the rollover from the March so don't don't get excited on that all right it didn't gap up 17 cents yesterday that that did not happen that's just when they see this what this means over here is when they roll over from one month to the next one okay now we had one other question and that was about I don't even know how to answer it but it's NVIDIA but I'll give you my two cents worth folks but that's and if you over pay it's your own fault so let me get rid of this out of the way here and I'll get rid of the corn out of the way here and what we want to do now is to come up here and look at the NVIDIA and I really I think no matter what NVIDIA does the stock goes lower that's just there's just too much hype if it if it's really really super bullish and believe me these things have surprised me in the past the time it gapped up $300 or whatever I say I can do that again there's no there's no reasoning why I can't because they got the wrong people on the wrong side of the fence it's going to be easy the weekly you know we're trading at $669 which is near the low of the week the low the week so far has been $666 ooh the devil's number so that's that's where we are right now the ABCD on this swing measures to $779 and that high was $774 missed it by $30 looking at this on a smaller time frame you'll see it's been coming down and it is following $382s folks here's the first breakdown there's your first three well it goes a little above the 382 there let's just go to the first break here there's the high and the first break takes you to the 50% level the second break is going to take you right to the 382 right there on the money honey there it is right there it's at one two three times and then we're heading down so they were the if the results come out and they could easily go up to $7 this thing could move $100 folks I think it's going to be frankly this is my two cents worth because I see this AI and how important it is but I wouldn't be surprised to see it jump $100 on either bad earnings good earnings whatever earnings it wouldn't make any difference wouldn't surprise me at all if it can do this look at this folks going back here on the daily any stock that can gap like this $150 in one day you can do it again so for God's sake you're going to short it use an option we'll be right back 877-976648 if you're looking for potential trading setups in the stock market then rocket equities and options report is a newsletter you should try Tommy O'Brien delivers options and equity trades when the markets present them using a combination of fundamentals and technicals sign up for rocket equities and options report today with a 30 day money back guarantee so you have nothing to risk for all the details and to start your subscription today visit the front page of TFNN.com TFNN Educating Investors everything in the universe is governed by the Fibonacci sequence this mathematical principle is responsible for everything from the most aesthetically pleasing artwork to patterns in the stock market to stay on top of stock patterns you can take advantage of sign up for the Fibonacci 24-7 newsletter at TFNN.com when you subscribe you'll get a weekly report from veteran day trader Larry Pezzavento on stocks you need to pay attention to and you can trust Larry's analysis after all he's got 45 years experience as a day trader Larry will also provide daily charts videos and data on the key markets that he's tracking expect notifications from Larry on market movement you need to act on at any time subscribers also get a 30-day money back guarantee if you're not satisfied let us know and you'll get a full refund within 30 days of signing up subscribe to the Fibonacci 24-7 newsletter today TFNN.com Educating Investors Are you ready to take your trading to the next level? Introducing Tom O'Brien's award winning newsletter Market Insights your key to successful active trading Tom O'Brien renowned for his expertise in the financial markets and market insights to be your daily guide to profitable trades Tom publishes his daily market insights newsletter every market day before the market open along with updates when warranted stay ahead of the game with Tom's real-time analysis and trade recommendations delivered straight to your inbox whether you're a seasoned trader or just starting out market insights provides the edge you need to navigate the markets with confidence ready to join the ranks of successful traders head over to TFNN.com and subscribe to market insights today don't miss out on this opportunity to supercharge your trading results market insights comes with a 30-day money back guarantee for all new subscribers so you have nothing to risk don't miss out on this opportunity to revolutionize your trading game head over to TFNN.com right now to join the thousands of traders who have already experienced the power of Tom O'Brien's award-winning newsletter market insights firsthand TFNN Educating Investors TFNN has launched the Tigers and hosted at discord TFNN has been educating traders for more than 20 years with live programming hosted by a variety of professional traders during market hours the Tigers Day available to all Tigers and Tigris for just one dollar for the year there's no cash or added costs when you join our community of traders sign up today and become a part of this educational community of traders just visit the front page of TFNN.com don't forget you can listen to TFNN live on your mobile device 24 hours per day go to TFNN.com and hit watch Tiger TV that's TFNN.com and hit watch Tiger TV okay folks I bought the bonds when the show started at 17.25 they've been as low as 17.21 I'm going to put my stop here at 17.18 that's going to be 8 ticks 8 times 320 is $240 I'm risking $240 I think we got a chance to rally from here the reasoning for that is because of this big ABCD pattern that measures right here 17.23 but if it goes much below that I don't even care just this more than I want to risk I'm not going to risk more than $250 8 ticks in the bonds this is the largest trading thing that we have other than notes it trades oh god just so many the bond pit was like watching three football fields but the biggest pit of all in Chicago was $1 which is US dollars traded abroad it was like two football fields stuck together you had to be 6 foot 5 and weigh about 280 and be stronger than a couple of Billy goats to stay in that pit because it was so physical they had paramedics there for broken stuff every day it was an animal pit is what it was anyway here's what we're looking at right here so have your stop working 17.18 and that your risk 8 ticks and that's more than you want to be working so that's pretty much it so tomorrow's guest will be Grace Morris of Astro Economics and on Wednesday of course we're going to have the Wizard of Astrology direct from Naples, Florida Norman who tells it like it is winsky will be our guest next week we hope to have Stan Harley as our guest also Bill Meridian and Jim Bart de Leoni from Barts charts will be joining us very shortly so those are just a few of the things that we have coming up in the near future keep that stop working folks because you don't know which ones are going to work and you shouldn't care because you never know which ones are going to work that's the bottom line so that's what we're watching for today so live every day in an attitude of gratitude and may God bless and I'll see you on the flip side come Monday


Hey, what's going on guys? Welcome to a new video. So today I want to share with you my top five picks for November 2021. So as we'll get closer to Christmas and of course, Black Friday, then time is running out to capitalize on the most profitable time of year. So in this video, I'm going to show you five proven products that are ready to start selling today. I understand how tedious and mind-numbing product research can be sometimes and how it can be difficult to actually judge a product and know what to look for. So in this video, I'm going to give you all the information you need to start selling these products today. That includes all the different validation points I use for any product, the Google Trends information so you know whether the product is in demand, the recommended selling prices so you know exactly how profitable they are and your Facebook ad target audience. And with that being said, thanks for tuning in. I hope you guys enjoyed the video and let's jump straight into product number one. So product number one is this heated scarf, probably one of my favorite products on this list actually for a couple of reasons. Number one, it's very similar to a past proven product. You may have seen me speak about the heated vests before my YouTube channel. They continue to sell every single winter here in the UK and their proven seven-figure products. I found a store on the exchange marketplace which made over a million dollars selling heated vests and this is the next best thing. We know from the past then that that heated clothing or heated items of clothing sell really well and with it being the winter time now and the UK is starting to get really cold then a products like this is only increasing in demand. To show you the search volumes in the UK from 2004 to present, we can see that pretty much nobody searched for this because they pretty much didn't exist until this year and just look at how popular they've become in November 2021. What's really great about this product as well even though it's brand new, what you sometimes find with brand new products is that when it comes to logistics and sourcing there isn't many supplies so they're difficult to get hold of or difficult to offer really good shipping options but that's not the case with this product. We can see they currently have stock in Poland, the US, the UK, Australia, France, Italy, Belgium and of course China. If we take a look at the video supplied from the supplier by the supplier, sorry, it's not too bad, it's okay. I'd definitely contact them and say, hey, have you got any more content? Have you got any more videos? Can you send it to me without the Chinese writing and so on and so forth but you could definitely chop this up and use parts of it. My ultimate recommendation though would be to invest in one yourself. You could perhaps feature in the video yourself or contact some influencers or even use ad creation services like Viral, Ecom ads and below just to make sure you go for user-generated content. What I also love about this product is it doubles up in terms of what it can do for somebody so not only does it keep somebody's neck warm where they're out and about walking but it also has health benefits as well. People who get stiff necks especially when the weather gets colder or a stiff neck and cold necks can be linked to headaches. This could definitely be a marketing angle for this product to help you sell it. With that being said, let's take a look at the numbers. So the cost is in and around 10 pounds delivered. Easily sell this product for 30 pounds I've seen it on some stores for over 50 which leaves a pretty healthy profit margin of 20 pounds. If you couple this with some heated gloves or a heated vest then you can be making some serious profit per sale. In terms of the Facebook ad interests that I recommend there's so many different ones it's really difficult to narrow it down just trying to think of people in the real world and what kind of application this product would suit.  Product number two is one of my favorites it's a dog sofa protector and I've actually ordered one of these products myself. This is definitely something I'm gonna look at drop shipping myself and perhaps even film a series around. The reason being is because there is such a strong demand for this exact product. What also helps is it's a product that's brand new for 2021 so there won't be many people out there who have seen this before. Your marketing angle at this is targeting people who have recently bought a new sofa as well as just your casual dog owners. Since the pandemic people have been spending a lot more money on things inside their homes.  And as we can see from this Google trend info more and more people have been buying sofas as well.   So this is where this product comes in to solve that problem and therefore it makes it in demand. What's also great about this product is it's a variation of a proven seven figure product. Late last year I uploaded a video of a Shopify store that had sold a plush dog bed and made over $2.7 million on that one single product. This product is very similar in the way that it's made out of the same materials. Looks the same but it's just in a different shape and has a different function and purpose. What I also love about this product is it's very reasonably priced as well. So the cost to us is £7.23 delivered. You could easily sell this for the very minimum of $24.99. Again, I've seen people selling this for a lot more which leaves a profit margin of £17.76. The dog niche during Q4 has got to be one of the easiest niches when it comes to upsell and cross-sell opportunities. So it wouldn't be very difficult to offer something else and bump up that average order value. In terms of the recommended Facebook interests I would definitely start with dog walking because that's the pain point which you're going to be solving or the result of a dog walk.  Product number three is also a variation of a proven seven figure product. If you think back to kind of Christmas time last year and there was that moon lamp that blue crate one of the big Shopify drop shippers at the time jumped on and so did quite a lot of other drop shippers and there was a lot of money made. What's great about this product is it's pretty much the same thing except it's for the child. So it's a moon lamp, it even has the same stand but instead of it being for an adult this would work as a great night light to go in a child's bedroom. And if they have a passion and interest in dinosaurs like most young children do then it makes a great gift or just impulse purchase for any parent or grandparent. The clocks have recently changed here in the UK as we can see from the Google trend info too more and more people are looking to buy lamps and as we come up to Christmas it makes the perfect lamp that can double up as a gift for somebody's child. In terms of the numbers the cost to us delivered to our customer is 11 pounds 15 the average selling price which I've found kind of across different platforms is 29.99 which leaves a pretty decent profit of 18 pounds 84. As for the Facebook interests I recommend for targeting definitely stick to parents with preteens parents with preschoolers and parents with early schoolers as well. If you stick to this age range you'll be targeting parents that have children between the ages of sort of three and 12 years old to really narrow down and increase your chances of finding that audience that has children interested in dinosaurs you could narrow down with such interests as dinosaur toys and Jurassic Park. Product number four is this memory phone relief pillow. The reason being is because since COVID a lot of these big companies are downsizing their offices because more and more people are working from home as people work from home they don't necessarily have the money to invest in a really expensive office chair. And so the next best thing is to spend only 50 pounds on a really high quality memory phone pain relief pillow that makes working at home so much more comfortable. This is also confirmed and proven in the Google Trends info. Just look at the recent spike of people searching for back pain and sitting. This is also a variation or a very similar variation to a proven past seven figure product. If we think back two, three years ago about the back posture correctors a lot of dropship has made a lot of money with them because they have a proven health benefit and it solves a pain point which is exactly what this product does as well. As for the numbers to cost to us to live to our customer would be 25 pounds. I would start the selling price at a minimum of 49.99 which leaves a decent profit margin of 25 pounds. In terms of the Facebook interests I would recommend I would start with neutral spine, spine health, home office, old age.  By sticking to these interests you're going to be targeting people who are working from home are conscious about their posture and potentially looking for an office chair to buy as well. Moving on to the fifth and final products which is my favorite one of the list which is this felt Christmas tree. Christmas time is obviously a time for the children and there's no better way to bring some festive spirit to the house than this felt Christmas tree which you can stick on your wall and allow your kids to pin all the different attachments and let your children decorate it. Now obviously I don't need to show you this but Christmas decorations are super trending right now and when it comes to targeting it'll be a super easy audience to target. In terms of the cost it's a really cheap product delivered to the customer is only going to cost you three pounds 83 but because of the enjoyment and perceived value of this product you could easily sell it for a minimum of 24.99. This leaves a great profit margin of approximately 21 pounds and 16 pence. As for the interests I recommend for this product I would stick to toys, online shopping, Christmas, Christmas tree, Christmas decoration and of course parents with children of certain ages. I can see children anywhere between the ages of two all the way up to maybe eight, nine or even 10 finding this fun and interesting. And so with that being said then guys I'm going to wrap the video up there. If you enjoyed this one don't forget to drop a like and of course if you want to see more of my content please consider subscribing as well. One final quick message before you go if you are looking for a course to help you get started and take full advantage of the Q4 period make sure you check out my Ecom Academy Clubhouse. Costs less than a meal out for two has over 150 premium and original tutorials and every week comes with proven products like the ones you've seen in this video. So if you'd like more information on that make sure you check out the links in the description below. Thanks again for watching and I'll see you guys in the next one.


Welcome back to Lecture 35, Part 2, The Wrath of Khan, in which case we are actually going to transition to Section 7.3 about duality from the Wallace and West textbook here. And so we've saw in the previous part of this lecture that in elliptic geometry, if we have a line, there exists this point called the pole, for which all lines from the pole to the line are equidistant. And also, if you're given any point, you can construct a line for which the given point is a pole to that line. And so this right here, this idea of the pole on a line in elliptic geometry illustrates a concept in geometry we refer to as duality, where a dual geometry, so given any incidence geometry, a dual geometry, it'll interchange the roles of points and lines. Because we define points and lines as, well, JK, we didn't define them, right? If we go back to the very axiomatic beginning of this course, points and lines are considered undefined terms, and incidence is just a relationship between points and lines. And so the dual geometry is formed given any incidence geometry, and it doesn't even have to be an incidence geometry. All that has to happen is if we have a geometry with a notion of point and line and incidence, we can reverse the roles. So you swap the roles of point and line, and you keep the same incidence relationship. This forms the dual geometry. And so this is a construction that works whenever we have points and lines, such as an incidence geometry, and you have other things as well, and this typically creates a new geometry of some kind. So I wanted to consider the order to affine geometry, the so-called four-point geometry we referred to earlier this semester. Now, in this geometry, we had four points, which in the diagram to the left here, you're going to see that you have this four-point geometry. We have the four points we'll call them P1, P2, P3, P4, as illustrated. And by line determination, there were six lines between these four points. And these were just handshake lines, two points per line. And so you can see the possibilities. There's L1, L2, L3, L4, L5, L6, right? L1 is the line determined by P1, P2. L2 is the line determined by P2, P3. L3 is the line determined by P3, P4. You get the idea right here. And so in the dual geometry, we could construct a so-called four-line geometry, which what we do is every point over here in the four-point geometry becomes a line. And so in this diagram you see right here, I've labeled, so in both diagrams, the points are labeled in green, and the lines are labeled in yellow. And so as we move from one diagram to the other, that color scheme is still preserved, but I kept the same names there. So the four lines you have is this one right here. I need a different color for that. We have P1, which now becomes a line. It's a line that contains the points L1, L5, L4. There's P2, which is a line that contains the points L1, L2, L6. There is the line P3, which contains the points L2, L3, L5. And then finally there's the line P4, which contains the points L3, L4, L6 here. So we have four lines in this geometry, and there are six points. In the original geometry, there was four points and there were six lines. So we have this duality going on here. We swap those, and let's discuss a little bit how this worked out. So the six lines in the original geometry L1, L2, L3, L whatever, those become the six points in this geometry over here, right? And then the incidence relationships are preserved. So if we think of, okay, what lines are associated to the point L1? Well, that's going to be the lines P1 and P2. So if we come over here and find L1, there you are. It has two lines incidence to it, okay? And then if we take the point L2, what are the lines incidence to it? Well, that's going to be P3 and P2. So if we come over here and find L3 right here, it'll be incidence to two lines. There's the line P3 and the line P2, right? And so you can carry this through with the other points and lines right there. So this is what we like duality. We switch the roles of points with lines and lines with points. We have the exact same incidence relationships, but we have a slightly different configuration of these two drawings right here. Now this one over here was an example. The original one was an example of an affine geometry. This is an affine geometry of order two. Not commonly used in the literature, but sometimes if you take the dual of an affine geometry, it's referred to as an if fine geometry. And not commonly used. You don't see that a whole lot. On the other hand, the first geometry satisfies the Euclidean parallel postulate. So some people might say this is Euclidean. Again, Euclidean as an adjective typically refers to as the geometry R2, but it does satisfy the Euclidean parallel postulate. A little bit more commonly used in this term if fine. Sometimes people would use describing this dual of the affine here. They call it Euclidean dual, sort of like just an amalgamation of Euclidean and dual right here. And so sometimes people use the term Euclidean dual to refer to as the dual of the Euclidean plane, but sometimes it's used to refer to as the dual of any affine geometry. So Euclidean dual is probably used more commonly. So this is the four line Euclidean dual to the four point affine geometry right here. I also want to point your attention that the reason I drew the four line Euclidean dual geometry the way I did is what happens if we were to overlay these two geometries? You place these two geometries on top of each other. You would get a picture that looks something like the following. I would draw it again. You get something that looks like the cloak of invisibility. We would get something that looks like the resurrection stone. And we would get three elder ones. Oh my goodness, this is affine geometry. If you completely overlay those pictures. Now there's a slight abuse there because we're identifying points with lines and such like that. But again, the configuration right here, you can see that just from a configuration point of view this overlay does give you the phantom plane. And this is actually not a coincidence that if you take an affine geometry and construct it Euclidean dual you overlay the two geometries. If you do this in a strategic way, you can actually construct a projective geometry. The phantom geometry is being an example of this. And the idea is actually the reason I mentioned this is that a projective geometry is actually an example of a self-dual geometry. Self-dual meaning that if you take the dual of the geometry, you get something isomorphic to the original geometry. That if you interchange the roles of points and lines it makes no stinking difference to the geometry whatsoever. So to try to make that more explicit, let's think about the following. Whenever you have a geometry, you can switch it to the dual statement. The dual statement meaning that you switch the roles of lines and points. So if we were to say something like, okay, in an incidence geometry we might say that there exists a point off a line. So we would write the statement in the following way. So for all lines, there exists a point off of... So when I say off of let's be more specific, there exists a point not incident to the line. So this is just a regular statement. We'll call it statement A for a moment. This is a regular statement in a geometry. And this is actually just the non-colonial axiom for incidence geometry. But this can be interpreted as a statement in a geometry. Well, we can switch to its dual statement, which we'll call A' which would say that for all points, there exists a line not incident to the given point. And so this right here is sort of a statement about non-concurrents. That given any points, there's not one line that is concurrent to all those points, right? And so this is what we call a dual statement. These statements are dual to each other, a dual statement. And dual statements, you just switch the roles of lines and points and like this. So whenever you have a geometry, which has a statement, whether it's true or false, you can rewrite that statement as the dual statement. That becomes a statement for the dual geometry. Now if you have a theorem, let's say this thing was like a theorem of the geometry, then the dual statement will become a theorem for the dual geometry with the exact same proof. And when I say the exact same proof, I mean the dual proof, you switch all the points to lines and the lines to points. And so one nice thing about duality is that whenever you prove something about geometry, the dual proof gives us the dual theorem for the dual geometry. You don't have to provide a new proof. You can just use the same proof, but you change by the principle of duality. Well, the reason this is relevant for projective geometry is that projective geometry is self-dual, which is to say that it's isomorphic to its dual. So whenever we make a statement in projective geometry, its dual statement also applies to projective geometry. That is, whenever we prove something in projective geometry, automatically its dual theorem would be true as well by the exact same proof. And this comes from the fact that the axioms of projective geometry are dualistic here, dualistic. So let's actually take a look at them real quickly. So if we take the five axioms of projective geometry as we have them before, let's take their dual statements, take their dual statements. So if we take line determination, which line determination, if you take dual, it would become point determination, right? So line determination says that for each two distinct points, there exists a unique line incident to both. The principle of duality here, the dual statement will switch the word points to lines and the word lined up point. So point determination tells us that for each two distinct lines, there exists a unique point incident to both of them. Now, this idea of point determination, it has a different name that we've used to before. We've talked about this statement. For each two distinct lines, there exists a unique point. Oh, this is just saying that all lines intersect and they do so uniquely. This point determination is none other than just the elliptic parallel postulate that we've seen in the past. Elliptic parallel postulate. It has a slightly different name, but the dual of line determination axiom is the elliptic parallel postulate, which is sort of an interesting fact to notice here. So if you take the dual axiom of line determination, you get the elliptic parallel postulate. Notice projective geometry already does that. All right, let's take the dual of tricancy. Well, tricancy says that for any elliptic or for any projective line, there exists at least three points on the line. The dual statement would say that for every point, there exists at least three lines concurrent to it. Because what does it mean for a point to be on a line? It means that the point is incident to the line. And so if we have a point and there are three lines on it, that's the incidence relationship right there. So while tricancy for projective geometry requires that we have three points on the line, the dual of tricancy just says that there are at least three lines incident to a point. Now, be aware that this type of property, dual tricancy, happens in projective geometry. Projective geometry does have this dual tricancy property. All points have at least three lines incident to it. So I want you to notice so far that point determination is a theorem of projective geometry because it's just the elliptic parallel postulate. Dual tricancy is also a theorem. That one's not immediate from the axioms, but one can prove and we've seen this before that it holds. What about line existence, right? Projective geometry has the axiom of point existence because that's just an axiom of incidence. Line existence would be its dual, that there exist at least three distinct lines. We switch the word point to line there. And you can see that a projective geometry, the smallest of all projective geometries of course is the phantom plane, right? Which has seven lines, but and every projective geometry that exists will contain an isomorphic copy of the phantom plane. It's the smallest example. So point existence, although the axiom line existence is a theorem of projective geometry. So this dual axiom is satisfied. Non-concurrents, right? We have the non-colinearity axiom that says that there is no line that contains all points. It's dual, which be the non-concurrents axiom. Non-concurrency here would tell us that not all lines are concurrent to the same point. That is there's no point that holds all the lines. And so there's always got to be a line that's not on a point. So you always have something like this happening, which kind of looks like the same type of picture we had before. But the point is the starting point with the non-colinearity axiom. We start with the line and we're guaranteed a point off of the line. With non-concurrents, we start with a point and then guarantee there's a line that's not on the point. And this is in fact a theorem of projective geometry so far so good. And therefore, the last one we're going to look at is the dual of elliptic parallel postulate. The elliptic parallel postulate says that all lines intersect, which if we rewrite that phrase in a little bit, we're saying that given any pair of lines, there's a common point incident to both. Well, the dual statement of that would then tell us that given all pairs of points, there's a common line incident to both. But wait a second, this right here, any two points, there's a line that's on both of them. That actually is just a restatement of line determination. Given any two lines, given two points, excuse me, there's a unique line between them. Now, the uniqueness statement was hidden up here in this point determination here. But because the elliptic parallel postulate generally doesn't take a uniqueness statement there because line determination gives it. I want you to be aware that this dual of the elliptic parallel postulate is holding here. So one thing to mention is that line determination and the elliptic parallel postulate are dual statements of each other. And so elliptic geometry gets these things. So these five dual projective geometric axioms are all theorems of projective geometry. And therefore any any so projective geometry is a dual projective geometry. But by similar reasoning, the projective axioms are actually also theorems of the dual geometry there. And so that's what we get that projective geometry is this. It's this self dual. The dual projective axioms are theorems of the projective geometry. Thus, any theorem that can be proven from the dual axioms can also be proven from the original axioms. This implies that for every incidence theorem and projective geometry, its dual is also a theorem of projective geometry automatically. And of course, you get the other way around as well. And so this actually helps simplify proofs in a projective geometry because we can use duality. Once you've proven one thing, you get the other one automatically. So like we want to prove, for example, there exists a set of four points, no three of which are collinear. The dual statement, there exists a set of four lines, no three of which are concurrent is automatically true in projective geometry if we can prove the original one. And I want to mention that this is a duality notion between points and lines. So points and lines are these dual notions. This is heavily studied in the literature. But if we go to elliptic geometry, which is a special type of projective geometry, there are other notions going on there as well. So like for example, the notion of duality can be extended to betweenness and congruence. And you should try to convince yourself that this idea of point betweenness, point betweenness if we go to like say neutral geometry or just an order geometry is dual with angle betweenness. We saw a lot of relationships between point betweenness and angle between, not my angle between this, I'm sorry, ray betweenness. Let me fix that ray betweenness. And there are some similarities going on there. And also in neutral geometry, we have this idea of segment congruence and its dual notion would be angle betweenness, not angle betweenness, sorry, angle congruence right here. Now, again, there's this duality going on here. So as we approach like the Euclidean plane, and then we look at the Euclidid dual plane, you'll see there's this duality. You swap not just points with lines, but you switch betweenness of points with betweenness of rays and congruence of segments with congruence of angles. And you actually get this very nice geometric structure going on here. And in elliptic geometry, these ideas of duality are also still self-dual. When it comes to, for example, a line in elliptic geometry, what is the dual of the line? It should be a point, but that's none other than just the pole of the line. This idea of polarity in elliptic geometry is just a tangible way of measuring this self-duality that happens in all projective geometries. We can specifically form a duality function that interchange every line with its pole and vice versa. This gives us a one-to-one correspondence like we talked about previously. So therefore, we can show that this correspondence and incidence and continuum we can do with betweenness and congruence as well is preserved. And we get this self-duality, a very strong sense of self-duality in elliptic geometry. Something that's absent from Euclidean and hyperbolic geometry. This idea of self-duality does not happen there whatsoever. Lines and points act very differently in hyperbolic and Euclidean geometry. But in elliptic geometry, lines and points act the exact same way. And there's really no way of distinguishing between the two except that we just so happen to call one a point and so happen to call one a line. And that brings us to the end of lecture 35. I appreciate everyone from watching this. If you have any questions, please feel free to post them in the comments below. And I'll be glad to reply to them sometime in the future. If you like this video, please click the like button, share with other people who would love to learn more about modern geometry as well. And feel free to subscribe so you can get updates about other cool videos all in the future. I'll see you next time, everyone. Bye.