So, we're just a couple of months into Trump's 2024 presidential campaign, and it doesn't really seem like he's thinking of ways to help the American people in the event he's able to win a second term.  Literally. So, this isn't the first report that we've gotten about his authoritarian plans for a second term, but basically, he wants to expand the death penalty, bring back arguably more barbaric ways to kill Americans, and on top of that, possibly make public executions a thing comparable to Saudi Arabia, perhaps. It's deeply chilling, but I mean, it's not surprising because this is Donald Trump who we're talking about. So the story comes from Rolling Stone magazine who spoke with three sources close to Trump on the condition of anonymity, and here's what they say, quote, the former president if re-elected is still committed to expanding the use of the federal death penalty and bringing back banned methods of execution, the sources say. He has even, one of the sources recounts, mused about television footage of executions including showing condemned prisoners in the final moments of their lives. Specifically, Trump has talked about bringing back death by firing squad by hanging and according to two of the sources, possibly even by guillotine. He has also, sources say, discussed group executions. Trump has floated these ideas while discussing planned campaign rhetoric and policy desires as well as his disdain for President Biden's approach to crime. In at least one instance late last year, according to the third source who has direct knowledge of the matter, Trump privately mused about the possibility of creating a flashy government backed video ad campaign that would accompany a federal revival of these execution methods. In Trump's vision, these videos would include footage from these new executions if not from the exact moments of death. The former president believes this would help put the fear of God into violent criminals, this source says. He wanted to do some of these things when he was in office, but for whatever reasons didn't have the chance. Hmm, interesting. So based on that, it seems logical to deduce that he's very heavily leaning towards public executions as a form of deterrent. In the same way that Saudi Arabia, for example, uses public executions to deter against political opponents doing disloyal things as one Saudi exile says the regime does. Now what I find hilarious about this story is that he's denying this. His campaign is calling this fake news when his Justice Department quite literally moved to expand execution methods for federal inmates on death row. So after his administration tried to expand the methods within which the state kills federal inmates and also expedited their deaths, by the way, he's saying, no, we wouldn't want to do this, but your administration tried to bring back firing squad. So why should we not believe that you would do that again? And it's not just firing squad to be clear. It's also guillotines and hanging and group executions and doing it in a very public way, which makes it really deranged. To be fair to Donald Trump, lethal injections is arguably more cruel and inhumane than death by firing squad. The authors explain Trump's firing squad fixation may address his desire for the dramatic, but some experts believe that an instant death by gunshot may be more humane than a lethal injection. There's pain, certainly, but it's transient according to Dr. Jonathan Groner, a professor of surgery at the Ohio State University's College of Medicine, quote, if you're shot in the chest and your heart stops functioning, it's just seconds until you lose consciousness. So even though death by lethal injection looks more humane and it makes us feel more civilized, it still causes suffering. And oftentimes it's botched and causes the inmates to die in a very painful way.  We should just not allow the state to kill citizens because if murdering citizens as a form of punishment isn't a violation of the Eighth Amendment's cruel and unusual punishment clause, then nothing is. So killing citizens should not be an authority that the state has. And on top of that, a reason to not kill citizens is because oftentimes we get it wrong. As Science Magazine explains, 4.1% or 1 in 25 death row inmates have been mistakenly convicted and this is based on three decades' worth of data. So when we get it wrong that much, when our track record is that bad, the state should not have the authority to kill people. And furthermore, this idea that using the death penalty as a deterrent is nonsense because it's not. That is demonstrably not the case. And I understand the emotional arguments that people make in favor of the death penalty, right? Yes, this one criminal, he murdered a bunch of people, did terrible things, therefore it's justified for him, so it should be an option. But even though I understand and sympathize with that argument, which is an emotional argument, but it is an argument nonetheless, the problem with that is that justification, those exceptions that we make are often used as a pretext to expand the state's ability to kill citizens and that ends up harming people in the future. So take this example with Rhonda Sanders, where he was asked about the Parkland shooting and here's what he said about protecting people in the future, specifically referencing the Parkland shooter and what he wants to do about capital punishment. We're going to reform the capital sentencing procedure in Florida. Of course, to get convicted of a crime, you need a unanimous jury. When Nicholas Cruz was somebody, everyone knew was guilty and he's entitled to process, but this was not anything that he admitted it, right?  How, what other penalty can you get other than the ultimate penalty? And yet you have one holdout that can nullify that. So DeSantis, Trump's main opponent, wants to expand the death penalty. He just said that. Now he may have said it in a more eloquent way and he used a more reasonable justification to do that. He doesn't want to expand the death penalty just for the sake of being cruel and seeking retribution. He wants to do that because in this instance with Nicholas Cruz, the Parkland shooter, it's obvious he murdered 17 people. We know he's guilty. Just put him to death. Like why are we even considering this? And I think that argument, it makes sense on a visceral level. The problem is that this short term justification will lead to long term harm because people will inevitably be harmed by this change that we're making specifically to punish Nicholas Cruz, somebody who's innocent will be killed potentially because of this change that we're making. So you have to ask yourself, what is the goal of our justice system? And if the goal is simply retribution, then that is going to lead to suboptimal outcomes as we've seen. We need to reimagine the ways in which we think about crime and punishment. Because if you want to stop mass shootings in the first place, being more harsher and punitive towards the shooters isn't going to stop the shootings, but gun reform will. Stopping drug dealers from dealing drugs by killing them, like Trump wants to do, isn't going to lead to the end of drug trafficking. Drug reform will. So we have to think about ways that we're trying to prevent crime. And if it's within the context exclusively of being more harsher towards criminals, that's where we're wrong and that's where the state should not have the authority to kill citizens. Because again, oftentimes it leads to more people getting harmed than we'd like to admit as a society. But either way, what Trump wants to do is deeply horrifying. And this is why we just can't allow him to get a second term, because we already saw how authoritative and he was in his first term. But now when he's like broadcasting what he wants to do and he's saying, I want to basically do public executions by guillotine or hanging or firing squad. That's where we've got to kind of wake up as a country and ask ourselves, how is this man viable politically in 2023? Even though, yes, the GOP base is insane and a majority of them support Christian nationalism, according to one poll. Still, I feel like this is a failure on all of us. Like this is a societal failure that we're witnessing that this man is still viable despite all the terrible things that he says and doesn't wants to do. So either way, that's Trump's plans. The best you can do is educate yourself and fight against him with everything that you've got. I'm chilling for the DNC. I stopped watching. So I definitely won't be hitting the subscribe button. Or turning on notifications by clicking the bell. No way. It's very sad, I know.


What's interesting about the current political scene, both in your country and here, is the way in which cultural politics has now moved to the front of the stage, so to speak, and in particular, and this is something I associate much more with the new left, than the right, particular obsession with language and the desire to regulate, control language, prevent people like you from even speaking. What do you think philosophically lies behind this? Yes, well, you know, so, what lies behind it is a rejection of the idea that reason is the mechanism by which we discover truth, that reasoned debate, reasoned argument is the way in which you convince other people, and using our mind, our senses, and our reasoning capability is the way we discover truth about the world. To one extent or another, they believe either in complete subjectivism or some kind of way in which truth is revealed to them by some mechanism. They know it, maybe it's through their racial identity or maybe it's through their intersectional identity, depending on who you talk to on the radical left, but once they have that truth, since they didn't achieve that truth through a reasoned mechanism, there's no way for them to explain it to us, and therefore the only way they can get us to come along is by using force. And this is all totalitarianism. You know, the communists can't actually explain to us why we should all be sacrificed, why we should all be killed in the name of the proletarian. There's no reason why the proletarians should rule and the dictatorship of the proletarians should rise. Or what even is the proletarian? Who are the proletarians? How do they make decisions? Because again, they get that through some kind of revelation and they get it through, the only way you get revelation really is through a leader like Stalin or Lenin who sees the truth, right? And they have to use violence. The fascists, how do they know what the Aryan race wants? Well, they get it. You know, somebody has to lead the Aryan race and have the revelation. And he can't explain it to us because he didn't get it through reasons, so he has to use force against us. The New Left is the same way. How do they know that this intersexual pyramid is the right intersexual pyramid? Not through reason, not through fact, not through logic. And once you abandon fact, reason and logic, you're left with force. So you're left with silencing people who are trying to use logic and reason to object to your stance. You're left with trying to enforce your beliefs on other people through force. And that's, you know, that's why philosophically, the thing we must fight for is reason and truth. The idea that truth exists, the truth, there is a truth, there is objective reality, and that the only way to know it is through reason. And if it is through reason and if there is objective truth, then I should be able to show you, I should be able to explain it to you, I should be able to argue about it, and I might be wrong, and we can have that debate, but using the tools of logic, not a fist. And it's when you abandon logic, when you abandon reason, a fist comes into the picture. So they're taking us, all these different types of authoritarian, are taking us back to a really pre-enlightenment period when at one point, you know, it was the Catholic Church or some other religious organization saying, we know the truth, and if you don't go along with it, we're going to burn you alive and torture you. And you have to sort of, you have to subjugate your own consciousness to the priesthood, or to whoever it is. And in a way, what we're seeing now is a reversal of this incredible liberating period that was brought into being by the renaissance, by the enlightenment, whereby individuals were then became free to utilize their own absolute cognitive capacity. And now we seem to be going back with these people. Well, I would say that what has happened over the last 200 years, really, since the enlightenment made these ideas explicit, and actually created a political system to manifest that, which is a free political system, whether it's American or whether it's Western European political systems that are free and respect free speech, because they recognize that reason is the only means to achieve, and therefore argumentation is the only means to achieve truth. But what we've seen is really from the beginning of the enlightenment, certainly from the beginning of the 19th century, that is the end of the intellectual enlightenment, what we've seen as a rebellion against it, whether it was conservatives in the 19th century, particularly German conservatives who resented the idea of individuals having opinions and individuals coming up with their own ideas, and individuals leaving the wonders of the farm to go to the city and be engaged in capitalism, or whether it's ultimately communism and Marx rejecting the enlightenment, or even Kant and Hegel is massively rejecting the enlightenment in his philosophy, but we see, coming out of Germany in particular, but also out of France, a real opposition to the enlightenment thinking. And I'd say the rise of communism and the rise of fascism in Europe are these pre-enlightenment ideas rebelling against the enlightenment. So they're new forms of sort of counter-enlightenment. Constantly we're seeing counter-enlightenment in the West, and we're constantly having to fight back against the counter-enlightenment, and unfortunately the enlightenment left a lot of holes philosophically that are being exploited by these counter-enlightenment forces. And one of I think Rand's contributions here is that I think she is the enlightenment philosopher of the 20th century. So she helps fill in the holes that the enlightenment created, that the enlightenment philosophers didn't fully articulate. For example, the enlightenment philosophers, many of them were quite religious, and she kind of brings a secular perspective and a secular foundation for a lot of these ideas. But we're constantly, and I think she provides us with tools to now continue the fight against the pre-enlightenment ideas. But this is the fate of the West, though, the fate of the world now, because Western ideas dominate the world. It's this constant battle between the enlightenment and the pre-enlightment. And in that sense, most of these ideas have a religious tinge to them. Communism had a religious tinge to it, fascism suddenly had a religious tinge to it, and you're seeing this new left ideology, and I'd say populism on the right, both have religious aspects to them, a priest to it. What do you mean by religious? Because I mean, many of the sort of modernist authoritarians of the 20th century, whether they were fascists or Marxists, certainly have said that they didn't hide against it. Sure. It was certainly God. They replaced God. Why religion? So they replaced God with another mystical entity. The communists replaced God with a mystical entity called the proletarian. Its consciousness, and how do we know what the, again, we need a leader to tell us. We need a pope to tell us what the proletarian wants. Fascism replaced God with the Aryan race or whatever, or the nation, right? Nationalism places the nation above the individual. And again, the nation is kind of a mystical entity. You see it in Putin right now. You know, the nation has kind of, the Russian spirit has kind of a mystical entity and you need that powerful leader to be able to tell you what is good for the nation and what you should do for the nation. And I think the new left has, in a sense, this mystical entity, this knowledge that somehow they have accessed, but it's fundamentally anti-reason. And when you don't have reason what's left, you have left emotion. And I would say that at the end of the day, religion is based on emotion. It's the end of the day. It's based on the truth as revelation, truth as coming, since there's nothing to reveal. It's ultimately the emotion. And so I think that all these supposed secular movements, by rejecting reason, are left with emotionalism. And in that sense, religion. And the state becomes a kind of an omnipresent or powerful agency that kind of replaces God. Yeah. So it could be the state. It forces everything. Or it could be the intellectuals, right? Yeah. It could be the intellectuals that tell you which group today you have to sacrifice. Right? Which group today is at the top of the hierarchy of need and therefore that require your sacrifice. But note that they've taken, in a sense, they've taken Christian morality. They've taken the morality of sacrifice. They've taken the morality of the neediest in society need your help or a group that they define as the neediest. Again, whether it's the parliamentarian, we must all sacrifice for the parliamentarian or whether it's the Aryan race, we must all sacrifice the Aryan race or whether it's transgender, you know, minority ethnic, this, that or the other, that we must all sacrifice too. There's always a group where morality demands that we give up our rights, give up our freedoms for their sake. And that again, I think, is religious, is religious based. All these people are put up on a cross as some kind of ideal that we must live, that we must sacrifice too. Thank you for listening or watching The Iran Book Show. If you'd like to support the show, we make it as easy as possible for you to trade with me. You get value from listening. You get value from watching. Show your appreciation. You can do that by going to iranbrookshow.com slash support by going to Patreon, subscribe to lifestyle locals and just making a appropriate contribution on any one of those, any one of those channels. Also, if you'd like to see The Iran Book Show grow, please consider sharing our content and of course, subscribe. Press that little bell button right down there on YouTube so that you get an announcement when we go live. And for those of you who are already subscribers and those of you who are already supporters of the show, thank you. I very much appreciate it.


All right. Here we go now. Welcome everybody. Lee Lowell here from smartoptioncell.com today is Saturday, January 15, 2022. Welcome to another edition of our Saturday Synopsis. What do we do? We look at the charts. That's what we do. We look at indexes. We look at individual stocks. I'm here to show you what I do and what I see on the charts. I'm a technical analyst. I study the charts. That's what I've been doing for the last 30 years. So I'm here to make these videos, these YouTube videos to try to help you understand what I'm seeing and how I could help you become a better technical analyst. It helps to have an idea of when to get in and when to get out of trades. I get lots of people email me asking me, Lee, how do I know when it's time to get into a trade? How do I know if I'm going to buy a stock? What's the right price? How do I know if it's overpriced, underpriced? I just don't know when to get into a stock. Now, in addition to fundamental analysis, which is what you can do to look at the underlying fundamentals of a company, meaning what are their sales? What are their earnings? What's their PE ratios? How are their projected revenues? Those are all the numbers that you can look at a company to see how they've been performing over time. But all those numbers are certainly a good thing, but it doesn't tell you when you should get into a trade or when a stock may be overbought or oversold or underpriced or overpriced. So for me, it's all about looking at the charts because all of that underlying data gets reflected into a price chart. Everybody that trades stocks has the same information that everybody else does. Unless you're an insider and you're getting some inside information, but we all know that's illegal, so we don't even talk about that. But everyone else that trades in the market has access to the same information. And all those numbers, all those sales, earnings, revenue, PE ratios, whatever, all gets reflected on the chart. And the market will tell you when a stock is overbought or oversold or when it's the right time to get into a trade. That's why I focus on technical analysis. That's why my main thing is 99% of the time, technical analysis is when I make a decision to get into or out of a trade. So I'm here to help you. I'm here to show you what I do, what I see and what I look for on the charts. And it's all about technical analysis and I'm going to show you what we use or what I use as my indicators. Now, whenever you look at a chart, you can look at a plain price chart. The price action is how has the stock been moving over time? Has it been going up? Has it been going down? And to help you along the way to help you figure out where's the momentum or if a stock has momentum or is it very choppy or is it moving in one direction, you can use moving averages and other types of technical indicators. Look at support and resistance levels. Where's the stock having trouble breaking through? Or where's the stock having trouble not falling below? Where's the support? Where's the resistance? So all these things you can look at on a chart to help you gauge whether it's time to get in or out of a position. Now, what you see here on the chart, I keep it very simple and very old school. I don't use a lot of indicators.  And which means every one of these vertical lines you see here is one day's worth of trading. And the top of the bar is the high of the day. The low of the bar or the bottom of the bar is the low price of stock traded for that day. And over time, it forms a pattern or it forms, you know, it has a direction. Now, what you're seeing on the chart here is what we look at for the overall broadest view of the market. And what we're seeing is the SPY, which is the exchange traded front for the S&P 500 index. The SP500 index to me is the broadest measure of the market as a whole. So I like to concentrate on that. And the SPY is a tradable fund, trades just like a stock. So it gives us an easy way to get long or short the market, whatever you feel. And it's a great vehicle to trade in. Now, for me, I have a long term approach. I'm bullish on the stock market for the long term, years and years and years. So to make it easy for me, all I do is when I want to invest in the market as a whole, I just buy shares of the SPY or I buy long term deep in the money call options, which is a subject for another day. But what I like to do is I try to buy the SPY on pullbacks. Whenever it has a decent pullback, I buy a few shares here and there and just do that month after month. And I create this long term position for my account. Now, I also get people that email me each week saying, Lee, I want to trade this thing. I want to get it in and out. I want to become a trader. So there's a lot of people that tell me what happens to their trades is that a lot of these people, they want to make money fast, so they're trying to trade very short term with options. They try to buy very short term call options, and those have a high rate of failure. Trading like that, it's a hard gig. It's very hard to do. If you're trading short term options, you've got to be really good at picking the direction of the stock because if the stock doesn't move in that short timeframe, those options that you bought are going to expire and you're going to lose your money. I'm sure a lot of people out there have tried it. That's not my game. I'm in for the long haul and when I do trade for our newsletters, our time frame is roughly one to three months, but we're trading out of the money options. That gives us a lot of cushion for directional error. That's what we like to do. We like to sell options because it gives us an opportunity to still make money even if the stock moves in the wrong direction. You really can't do that. If you're buying stocks, there's only one way to be right and that's the stock has to go up. Or if you're shorting stocks, there's only one way to be right and the stock has to go down. If it moves in the opposite direction, you're toast. We like to sell out of the money options. That gives us a lot of cushion for directional error because we all know we're not going to get the direction right all the time. You might as well play and put the odds in your favor by selling out of the money options because it gives you a lot of cushion for error. That's how we do it. That's how we do it. Let's take a look at the market and see what's going on and give an idea of where it might be heading next. On the charts, I have my three normal moving averages. I have a 20-day, 50-day, and 200-day moving average. Those are up here on the price action. Down here, I have the 14-day RSI overbought, oversold indicator. I got the 80-level, 20-level as my overbought, oversold levels. Down here, I have the stochastics, which I've recently added. Just trying to see if it could help me time my trades a little bit better. I don't know if I'm going to use it long-term. I'm giving it some time to see if it can help me. Anyway, this is the stochastics down here. The numbers are 12, 26, and 9 because when you pull up the stochastics, you have to put in some levels. 12, 26, 9. On the RSI, it's a 14-day RSI. Let's take a look at the market and see what's happening here. I have these markings on the charts that I've kept for a long time. I'm going to take these off now so we can kind of look at more of the price action without all this mumble jumble on here. I've had these lines in here for a very long time. For some of you that have been with us for a while, you know you've seen these patterns here. I'm going to get rid of a lot of this stuff. We can start from a nice clean chart. You can see this W pattern, which is a bullish pattern. Obviously the market went up at that point. I'm just removing all this. Now we have a nice clean chart. You can see just the beautiful momentum, the upwards momentum the stock markets had since the pandemic. I'm going to pull back a little bit here. Here's February, March, 2020. Had the V-shape recovery and the markets just gone up since. You've been in the market long-term bullish.  Now if you're trying to shade this thing short-term, you may have been whipped out back and forth, back and forth. I'm just trying to tell you if you're trading short-term options, it's a tough gig. So where is the market headed? Well, obviously you can see it's going up, but a lot of people get caught in these little pullbacks right here. One to two-week pullbacks, people get nervous and they sell out of their positions and they get frustrated because the market has a little bit of pullback for a couple of days. But if you think about it, the stock market is at all-time highs. We're going to pull out to the monthly here. You can see the S&P 500 all-time highs just this month alone. Back here on this was the first couple of trading days of January, hitting all-time new highs. Let me open this up a little so you can see it better right here. So this was on January 4th, right here, all-time new highs. So if you look back, the market's been great and we're trading at all-time new highs, but it's these little tiny pullbacks that get people all crazed. They think that this is the start of the next bear market and they bought their call options up here on the tops and the short-term call options they bought. A couple of days later, those things expire and people are losing money. So they get very frustrated. That's not how I like to play. That's not how we play it in our newsletters. We're just going along with the momentum and we're looking to buy or we're looking to get into our long positions. Those are selling put options and selling put option credit spreads. Those are bullish positions. So we look for the pullbacks and then we enter our trades. Well, how do we know the market's on a pullback? Well, that's when we start to draw our trend lines. So I'm going to just start drawing some new lines here and I won't go all the way back. So you kind of connect the bottoms of some recent moves here. So here's your little uptrend on the bottom of the channel and I'll just connect some of these lines up here. It doesn't have to be exact and what I put on the chart might be something different than somebody else might put on the chart. But right now you can see that the S&P 500 or the general market is sort of now in this little uptrend for the last three or four months or so. So if the market goes along with the pattern that it's been, and I say this a lot, an object in motion will tend to stay in that same motion until something comes along and knocks it in another direction. And stocks trade the same way. They trade with momentum. They're going to keep going in that same direction until something pushes it in another direction. Now that push could be a one or two week down move or it could be something like the pandemic where it pushed it really far down. But for now, we're in this nice little channel here. So you can see when it connects to the bottom leg of the channel, it will tend to go up. It's not guaranteed. There's no guarantees in trading, but you want to pick higher probability entries. So here is a more higher probability entry or anytime that the market, the price action has come down to the channel. Or on other times you can see the price action bounces every time it hits the 50 day or the 20 day moving edge. Here's the 20 day, the blue line, 50 days, the red line. So if you're trying to try to gauge your timing, you can gauge it off of the moving averages or you can draw yourself some channels like this. Now what I've been doing is I nibble. And when I say nibble, I buy a few shares here and there of the SPY. I just keep building my long term portfolio, but I buy in dips. Okay, I buy in these dips down here. Today I bought some more of the SPY right around 460. Right around 460, I bought some and the market closed at 464.72. I'm not scalping. I'm not selling these things out. These are things that I'm holding for the long call.  So I keep building this position. And, you know, one of the times I bought here, we'll look where it is now.  Now, if you want to short the market or sell the market, you could try to sell it when it hits along the top leg here. But you got to be fast because the market is meant to go up over time. So if you're short and you sell, you better take profits pretty quickly or else they're going to evaporate because the market is just going to keep going up over time. So what we do in the smart option seller, we look at the charts. We try to time these entries here. When it looks like it may be bouncing off the bottom leg here, that's when we enter a naked put sell or a put option credit spread, which is also a bullish strategy. So that's what we do. And that's as simple as that. Now, the RSI is, you know, right in the middle of the range, it's not overbought, not oversold. So that just tells me the market is content and it's just moving up nicely along its nice momentum. Stochastics here, you know, not telling me all that much. If anything, it may be getting a little on the overbought side, but the RSI is not telling me that and the price action is telling me it probably could bounce here. So I'm not convinced that the stochastics is helping me enough. So I'm not sure if I'm paying, if I'm going to pay a lot of attention to that. But anyway, so for me, once again, I nibbled here the other day, I nibbled down here. A couple of weeks ago, I nibbled down here. And that's just how you can build a long term position. If that's what you want, I'm not telling you what to do. This is not, I'm not giving you any recommendations. This is not personal investment advice. This is just me telling you what I've been doing. Okay, so here's the the S&P 500. And I think it's going to keep going up over time. That's just how the market works. Sure, there the narrative out there is an inflation is creeping up or it's been creeping up. It's been very high actually, you know, things cost more money these days, everything that you buy. That's just what's happening out there. The US Federal Reserve is going to start raising interest rates to help fight off this inflation. And typically stocks can sell off when interest rates rise. But we know interest rates are not going to rise dramatically. They come in little baby steps, not enough for you to pull your money out of the stock market and start investing in long term, you know, US Treasury bonds. Those still don't pay you hardly anything. It wasn't going to give you 2%, 3%. Whereas in the stock market, the long term average is somewhere between 7% and 10%. If you look at the S&P 500 over the last couple years, it's been returning 27%, 28%. It's been crazy. So the stock market is still your best bet for long term, long term wealth. So if the Fed starts to raise interest rates, you're not going to see this gigantic sell off because people know better. People are smarter than that. So the stock market is meant to go up over time.  It's just too hard of a way to make money. So I'm in it for the long haul. For our newsletters, we're in one to three months at a time and we sell out of the money options because it gives us more directional cushion for error. All right, so let's take a look at the NASDAQ represented by the QQQ and the tech stocks have been having a little bit harder time of late. Now you can see I've marked this up pretty good as well. We've got this long term uptrend, which has been very nice as well. You've had some pullbacks here. It's been sideways here. So let me open this up a little bit. So I probably drew this, this little channel very recently. So it's been bouncing in between this little channel fell through it a little bit this week. Pop back up and then you can see here to yesterday on Friday, it closed. Here's a little dash mark on the right side of the bars where it closed for days. So it closed above the bottom leg of the support here. So maybe next week, if the news is not that bad, maybe the NASDAQ will pop here and head back up. Now, if you're looking to get long, you're looking for higher probability trades. This is where you might want to nibble a little bit. Not saying to bet the farm, don't bet the house, but there's a good possibility that the NASDAQ could bounce because it's following along the patterns. And this long upwards pattern is still intact. If you just extend this long blue line, you'll see it matches up right with the bottom edge here. We can take this off and we can draw a new one here. We can go back as far as you want. So you just kind of connect some of the bottoms and there you go. It's still within the long, long-term channel there. So you're looking for higher probability setups. The market's still going up. Maybe you wait for it to come down a little more to see if it bounces. If it bounces, then you get in. You may never get the bottom, but you'll get it on a nice move up. So the market, to me, looks good for the long haul. That's just how it works. You're going to have fits and starts. It's going to go up, it's going to go down, but you have to be willing to see through it. You have to be willing to get through those times. If you're playing very short-term trading, you better be super good at picking direction in the short-term. You better know where the stock is going in that one week timeframe. And that's very hard to do. So just be careful if you're playing short-term. So the NASDAQ's still going up, going through fits and starts. Are we going to have a bear market? Because there's always bears out there. There's always people saying that we've hit the top, we can't go any higher. And why do they say that? Because they're probably not in the market and they're just wishing the market will come down so they can get in. Or they're just, they don't know any better. So they could have said, we're never going up again. And after the pandemic, they said, we're never going higher than this and they've tried to sell here. And they try to sell here and they try to sell here, but yet the market keeps going up on them. So the bears have been losing pretty badly. So the broader market, the NASDAQ, the S&P 500, even the Dow, we can look at the Diamonds DIA. That's the exchange-traded fund for the Dow Jones. Dow Jones going up as well has a nice movement up higher. And the market, the overall market is going to keep going up as well. So we look for the pullbacks and we get into trades. Now, we did sell a put credit spread on the QQQ this week. Can't tell you the exact specs of the trade because that would be unfair to my paying members. But we're using the pullback as an entry, as a bullish entry. And we're hoping that the market will go up, which will make our trade work out. These are higher probability setups that we're looking for. All right, so let's take a look at some individual stocks because that's what we do as well. We trade individual stocks too. And we always tend to look at some of the same stocks because these are the stocks that we trade. And I pull up some other stocks just to show you some patterns. So let's look at Apple first. Now, you can see that I have tons of things under here. I've got channels and triangles and W patterns, channels. So where is Apple looking? Well, Apple had just hit all-time highs again right around the beginning of January, along with everything else, had the pullback. And now it's sort of trying to find its footing here. Is there a pattern that I can see? You always want to try to look for patterns. What I can see here is maybe we've got some support right around here. Support comes when a stock makes a number of moves to a certain area where it can't get through, whether that's trying to get up through resistance or trying to drop through support. So around the 168 level seems to be a bottom for now. Is there any other pattern I can see? Apple is still on this nice little uptrend here. And maybe we have a little resistance up here. It's forming this ascending type of triangle here within a sort of a sideways pattern. It still has the momentum. So maybe it's going to bounce off of this trend line that I just drew and maybe it'll start to go up. And maybe it'll try to get through this resistance line right around 182, 183 right up here. So you can see Apple's probably going to move along this bottom leg of the trend line and try to get up through this resistance. Or if we have really bad time in the market, then it's going to drop down through the support and trade somewhere in between the 50-day and 200-day moving average. So those are the scenarios. These are the things I look for. Try to gauge which way the market or stock might go. So to me, if the market is strong next week, Apple's going to move along this bottom leg here. So people say, when do I get in? How do I know it's a good price for a stock? Well for me, all those fundamentals I talked about are reflected in the price chart. So it's all about trying to find the higher probability setups, where the stock may go next. And if you want to get along the stock, then you wait for that point where you think it's going to bounce. That's how you do it. So that's Apple. Let's look at Tesla. We look at Tesla every week.  I talk about it all the time. It's very hard to chart. Sometimes it's very hard to drop a chart on Tesla because it's very erratic. It's very volatile. For right now, maybe it's in this little downtrending channel, but it popped above it, popped back down, popped above it again. So this channel, maybe it's not the greatest thing to look at. It's hard to sometimes gauge where Tesla might go. We may have the support right around 900, could be good support right there. I'll draw the line, make it long so we get some time here. If Tesla does come back down this week or next week, it would probably find some support right around 900. And we'll see. So the moving average, the 200-day moving average is sloping up the R-size. Right smack in the middle, Stochastic's right smack in the middle. So Tesla's not oversold right here. It's just probably going to move along, maybe along with the downtrending chart, or maybe the downtrending line, or maybe it'll just start to go up again. For me, it's very hard to gauge where Tesla wants to go next. The technical tools I use, sometimes it's hard to apply to Tesla. That's just the kind of stock it is. So that's Tesla. Let's look at some others. Let's look at Disney. We've looked at Disney before. Like Disney down here, bought some off the bottom of the R-size. I got real oversold, the Stochastic started to turn up from there as well. Kind of meandering along here, but had a big down day today. So it's been knocked back down. Where's Disney going to go from here? It could be anybody's guess. Could be starting another downtrend here, maybe a little bit. But we know in the long run Disney's going to go back up. Going to find its supports at some point and find new highs. What I get in here, I don't see anything that's telling me one way or the other I should get into Disney, either on the long side or short side. I'm not doing anything on Disney because the chart just doesn't look right for anything. If anything, Disney might sell off a little bit more. The R-size turned lower. The Stochastics may have a crossover to the downside here. So staying away from Disney for now, nothing there for me. Let's look at Walmart. Walmart is in this longer sideways channel that I drew here. Got the upside, got the downside. It's right in the middle. Some people could say, we also have, you've got a triangle pattern, congestion pattern right here. What does that mean? That means that the ranges are getting tighter and tighter and eventually it's going to blast out either to the upside or to the downside. That could be one scenario or the other scenario is it could just, you know, trade, keep bouncing in between the channels here. But for now, this congestion triangle pattern, Walmart will probably blast out to the downside or the upside pretty soon. And I'm hoping to the upside because I'm long some Walmart for the long term. I want to see it go up, but there's no way of telling yet. Now we do have earning season starting next week. Earning season is getting underway, so the next month and a half is going to be a lot of earnings. So we're going to see lots of companies moving big in one direction or another. All right, so we got Walmart. Let's look at Clorox because I've been talking about Clorox. I have a position in Clorox and I had mentioned a few weeks ago that, you know, let me pull back here a little. So I show every week Clorox was in a nice uptrend, was in this nice downtrend. It finally was trading sideways for a while. I was saying, okay, as soon as it gets out of this sideways channel and gets above the 200-day moving average, I'm getting in. Okay. And right here, this section right here, around the middle of December, I bought in around $176 a share. I thought that was going to be the breakout and would just go higher from here. It came back down into the channel, but found the support at the uptrend in 20-day moving average. And now Clorox is looking pretty good. Had a good day yesterday, Friday, January 14th. So I'm in the black here, which is good. I think Clorox should probably keep moving higher from here. What other stocks do we like to take a look at? Pepsi. Coke and Pepsi we'll look at. Pepsi still looking strong. Just has this nice, beautiful following along the trend lines. I think this is all-time highs for Pepsi. Let me take a look. Yep. All-time highs for Pepsi. Pepsi just has this nice, just beautiful, beautiful, just hugging along the 20-day moving average. Pepsi I think could just keep running higher, just going to follow along on the moving average. But just remember, if you get into a trade, keep an eye on when earnings are. We don't like to have positions over an earnings announcement, so we keep that in check. Let's look at Coca-Cola. I think we just hit. Let me double-check the monthly chart here. Yep. All-time new highs for Coca-Cola right here. Just today, I think it was. I'm long Coca-Cola shares. Good dividend. All-time new highs, the end of yesterday, Friday. So Coke looking strong. I really can't see any reason why it would come off from here. All right. I wish I could get a trade going naked put-selling, but it just doesn't offer me enough downside cushion when we sell put options. But Coca-Cola, great long-term company for long-term. What other stocks? AMD. We always look at AMD. AMD's been pretty erratic of late. The tech stocks have been getting hit. AMD's part of that. Coming down, get down to this 130 level that I drew support line. I don't remember when I drew it, but obviously we had a big blast through it here. But this was the end of last week, I think, and had that nice reversal. Had that big reversal day, which was nice in the market. And so AMD is now back above the support line. It may have a little bit of a down trend there. Some people would see this as a bearish type of pattern where it's going to keep trading in here and then eventually fall through. I don't know yet. I'm keeping an eye on AMD. We don't have any trades in AMD at the moment. I'm just waiting to see where it goes. Let me take a look at my stocks here and see what else I have on the list. Let's see. Oracle, let's take a quick look at Oracle. We've had a put-selling Oracle that has moved in the right direction for us, even though the stocks come down. We got into Oracle right around here. It had a nice bounce, and then it pulled all the way back. So we got in right around here somewhere. We sold the put and the market and the stocks hasn't really gone much. Hugging along the 200-day moving average here is the cast is kind of hugging along the bottom. Probably going to find support hopefully and move back up. I like Oracle for the long term. We sold the put on it with a lot of cushion, so that worked for us. Let's look at Cisco. You know, not seeing much there. Cisco, let me move this over. Let me move the title over a little bit. And not seeing much in Cisco. Let's take a look at what else we got here. Whoopsie. Hang on. Sorry about that. Saw my emails in there. Let's take a look at some other stocks. We looked at Disney, Walmart, Tesla. Now the healthcare stocks have taken a little beating this week. Not BMY, though. Pfizer, Merck. Healthcare looks decent. Kellogg. And let's take a look at Kellogg here. Kellogg's had this nice sort of roundish bottom and starting to move higher. Kellogg and General Mills. They kind of grouped them together, make a lot of cereals. They've both been moving higher. You know, just kind of hugging along their 20-day moving averages. What else we have? Verizon I talked a lot about as well. Had the bullish move finally off the bottom. Had a bullish flag pattern did go up. Maybe making another bullish pennant here could be possibility. Will Verizon bounce right off the 20-day moving average and move higher from here? I'm watching Verizon next week, actually. And see if it bounces here and goes higher. If it is, I may start to nibble here and may get us in for a new trade. So that's Verizon. Same thing with AT&T. AT&T had actually a bigger move. Went from $22 to $27 a share. So they're moving in tandem. Let's take a quick another look here. What other stocks we have? The payment sector. PayPal and Square. I've talked about them as well. PayPal. It's been trading sideways here. I don't like this last little move here. It's sort of getting through the support line. You know, PayPal could have a few more days of downside. I don't like how it kind of fell through that 180 level here. Keep an eye on PayPal. If you long, you may want to tighten up those stops possibly. I'm going to give it a few more days. The RSI is still sort of in the middle, but could be in the stochastics, could be starting to turn down. We'll see if it crosses over next week. Square, the other stock in the payment sector. Getting beat pretty good. Getting beat pretty good. Price action still going down, but the RSI is just kind of hugging along the bottom, not making new lows as the price action makes new lows. That's sort of a bullish divergence. I'd like to see Square kind of find a bottom here. The stochastics kind of hugging along the bottom also. So maybe the selling is starting to dry up in Square, but I'd like to see it trade sideways for a little bit, and then it should start to move higher. All right, let me see if there's anything else here. Let's see. What do we got? Twitter? Twitter still kind of, Twitter still going down. I'm not sure Twitter's found a bottom yet. Still going down, but the RSI hasn't made new lows either, and the stochastics still kind of going up. So maybe Twitter's getting close to a bottom there as well. Let's see what else. Anything else that strikes are fancy. Facebook just going along. Chewy. Chewy's kind of stuck in a downtrend here. Still in this downtrending channel for Chewy. Chewy might have a little bit more to go on the downside. Bitcoin stocks, Marathon, Mara. Bitcoin doesn't get going. These are going to drop a little tube. Riot and Mara. Riot kind of falling through the support that I drew there. All right, I think that's about it. We look to Coke. We look to Clorox, eBay. Anything happening in eBay? If anything, you might have a little more to the downside. All right, so that's it for the synopsis here. These are just things that I'm seeing. Get good with your technical analysis. Start looking at charts. Start looking at support and resistance. Start seeing where the moving averages are, and it'll help you with your timing. It'll help you time your trades. It's just another tool to have in your toolbox if you understand how to do technical analysis. All right, so that's it for that. It's been helpful to you. Let's quickly go to our website. SmartOptionSolo.com. You know we talk about put selling a lot here. So go to our website. Click on the put selling basics, our website, smartOptionSolo.com. Click on put selling basics. We got a free copy for you. Put your name, email, address here. Send your free copy. What else we have here? Our services tab. We have our two newsletters and our one-on-one coaching if you need some help getting to the next level. All right, so that's it. That's all for this YouTube video. Leave me a comment if you would. Don't forget to subscribe. If you'd like, hit that red subscribe button in the bottom right-hand corner. And leave me a message. Send me a message. Email me. I love hearing from you. And I will always try to answer you back. All right, that's all for me today. Hope everyone has a good weekend and a great trading week ahead. And I hope to see you back here next Saturday. All right, this is Lee Lowell signing off.


So, today we shall start talking about a new concept which many of you have seen in the context of Euclidean spaces presumably, but we will introduce it more formally particularly for more abstract vector spaces that we are now going to handle and deal with in this course. So, the idea is of linear independence all right. So, when do we say a bunch of vectors is linearly independent and you cannot get a vector out of some linear combination of other vectors sorry okay, but I would just want to visit that point what another of your friends has mentioned because that is quite interesting. So what can you say about this particular set suppose this is the vector space and I plucked out this vector. So, how does your definition work for this you see that is yeah but then you are adding more clauses right just now you said that if a vector cannot be represented as a combination linear combination of other vectors then we are done but that is not it. So, we need to be more specific and precise about the way we define things which is why we will go for the following description which is to say that if a non maybe hyphenated word non trivial linear combination of vectors in a set S which is contained in the vector space V does not or rather if let us let us take the opposite because I have kept that provision open. So, it is an easier definition and we can say does lead to then what do we say about such a set. So, what is the attribute of it is an attribute of a set of vectors whenever I talk about the property of linear independence or linear dependence I have to know what sort of object hand categorizing it is a set of vectors in a vector space whose linear independence or dependence is being debated right. So, what do we say in the other this case if a non trivial. So, of course, this non trivial I have not defined or described yet but hopefully you understand we will describe that do not worry if a non trivial linear combination of vectors in a set leads to a resulting vector that is this then what do we say about that set right then S is linearly dependent now of course, conversely if no non trivial linear combination can ever lead to the 0 vector right then it is linearly independent right. So, that is what the description is. So, never ever try to define this linear independence by saying one vector represented in terms of the other vectors that is not necessarily true particular case being when you have the 0 vector. However, this definition accommodates everything all possible eventualities are covered here in right. So, I will give you one example of something that you may not view as a vector at first glance because you normally think of n tuples as vectors. But let us say I consider the vector space to be. So, when I write this it means this is a vector space of polynomials of degree 2 or less whose coefficients are real numbers right that is the notation. So, this is a vector space you can go ahead and check that it satisfies all the properties of vector spaces. If you understand what addition of polynomials are in the conventional sense and what multiplying a polynomial by a real number is. So, of course, this is over the field of real numbers right now consider the set note that these are all members of this vector space right. The claim is that this is linearly independent how do we show this the multiple ways of showing this any one way of showing if this is linearly independent if not then let us try out. So, C0 times 1 plus C1 times x plus C2 times x squared suppose this is equal to the 0 polynomial the identically 0 polynomial note this is not an equation I am writing ok. This is the polynomial and this is the 0 polynomial there is a difference ok. If you look at it like that without any context and all of this structure you might think this is a quadratic equation no it is not a quadratic equation I am saying that there will have to exist some C0, C1 and C2 some real numbers. So, let us say C0, C1 and C2 are some real numbers if I can find out some C0, C1 and C2 some real valued C0, C1, C2 that results in the 0 polynomial then I will show that I will have shown that this is linearly dependent. But the claim is that this is linearly independent so I should somehow be able to show that this can only result in the 0 polynomial if this is yeah this all these 3 have to be 0. So, of course, because you know that over the real numbers this polynomials are differentiable you can just go ahead and use the fact that this has to be true for all x because it is 0 in the sense of the polynomial remember. So, it is true for all x right that is the idea of linear independence in this case. So, this must be true for all x so in general if it is true for all x specifically it must be true for x is equal to 0 if you plug in x is equal to 0 you are led to conclude that C0 is equal to 0. And then you can of course go ahead and differentiate but there is another way of seeing this you see because you know that over the real field one must exist which is a multiplicative identity. So, once you have established that C0 must be 0 then you are left with C1 x squared C1 x plus C2 x squared must now be 0 now go ahead and plug in x is equal to plus 1 and what you will have is C1 plus C2 is equal to 0 also in the field you know in the real field that 1 exists minus 1 also exists. So, you can go ahead and plug in minus 1 so this is for x is equal to 1 and finally for x is equal to minus 1 you can just take minus C1 plus C2 is equal to 0 already you have seen C0 is 0 now of course based on these it is immediately apparent that both C1 and C2 must also be 0 and therefore, the only way to result in the 0 polynomial identically for all x using these vectors from this vector space is to choose C0 C1 and C2 all three of them to be equal to 0 and therefore, this set is linearly independent right is that clear. So, this is an example of a set sitting within a vector space which is linearly independent which looks nothing like the n-touple of numbers right ok. Having understood this I will make a couple of claims or maybe 2 or 3 claims and I will argue that this these must be true ok. So, suppose S this is a subset within a vector space I am not writing this you by now you understand when I write this as a V it is a vector space ok is linearly independent writing the shorthand for any S bar which is a subset of S we have that S bar or rather S underlined is also linearly independent is this obvious how do we go about trying to prove something like this a claim such as this once again we try to contradict this. So, we try to assume first that suppose S bar S bar which contains at most all the members of S in which case by definition it is linearly independent, but if it contains fewer fellows than S let us assume that S bar contains some of the fellows that are there in S not all of them because if it contains all of them then it is just S and S is by our claim linearly independent nothing to prove them. But suppose S bar S underlined contains some of the fellows of S only and that some of them are not contained in S underlined the subset if despite that it turns out that this S underlined this set is linearly dependent then is it possible that S can still continue to be linearly independent right. Because if there is a non-trivial linear combination of fellows here you might just as well go and append the fellows that are not here, but here with coefficient 0 you will still have a non-trivial combination non-trivial combination means at least one of those coefficients is non-zero. Now as long as you found some of the fellows here to have non-zero coefficient you might as well pad the rest with 0 coefficients it will still be a non-trivial combination. So, it is not possible that any subset there of a subset of a linearly independent set has to also be linearly independent right and by the same token kind of a converse relationship suppose S contained within a vector space V again I am not okay let me just mention that this is a subset is linearly dependent. Now for any S bar which is contained within sorry which contains S and of course S bar is also of course it is part of V right linearly dependent. So, for any S bar within which this linearly dependent set is sitting yeah we must have S bar as a linearly dependent set. I mean already it is defective defective in the sense that it has lost its linear independence within S, S is already linearly dependent. So, any super set of a linearly dependent set must be you cannot build a structure on weak ground right you already lost linear independence in the set S itself you cannot hope to extend it to a bigger set which contains everything that is there already in S and still hope to build a linearly independent structure out of it linearly independent set out of it right. Once again you can just try and fill in the arguments here just a couple of lines you have to just assume that there are certain fellows belonging here certain fellows belonging there and so on right and take combinations and argue. So, I hope that these two assertions are very clear and a third and important most one of the most common assertions which we started this discussion with is this any set S contained in the vector space V which contains the 0 vector must be linearly dependent. Again very straight forward a ready made choice ready made choice for a non-trivial linear combination is just attach some non-zero coefficient to the 0 vector and attach a 0 coefficient to all the other vectors that is a non-trivial linear combination of fellows sitting inside S which results in 0. So, this must be true any set that contains 0 can never be linearly independent 3 claims that we have made we have not even sort of dirtied our hands by trying to prove them, but hopefully we have presented arguments that have convinced you that these 3 are true. So, that is the first important concept we have introduced today which is that of linear independence or linear dependence the complementary properties. So, once you understand one you understand the other any questions so far no S bar is a superset of S yeah S bar is contained in the vector space of course. Why not? So, S bar this is a vector space. So, S bar contains only fellows that are qualified as vectors within the vector space V. So, I mean why not? So, for example, let us say you have 1 x 2 x x squared alright and you have 1 let us say 1 x x squared that is it and 1 x 2 x x squared and let us say what should I write 5 x squared 5 x squared yeah should I say let me just add a random number of elements here 7 x 3 x squared 5 x squared yeah and let us say this is 2 x ok. So, already this is linearly dependent set see these are all coming from that example that I had given the vector space over R this is a linearly dependent set why because I can identically cook up just these 2 fellows here yeah.  So, that is a non-trivial combination that leads to the 0 polynomial therefore, this is a linearly dependent set now this one contains every fellow that is here. So, this is my S and this is my S bar now you see S bar must come from this as well that is all that I am saying now my vector space is this this is the V right that is all that I am claiming. So, therefore, if you cook up a super set of a linearly dependent set to begin with that super set also must be linearly dependent because otherwise it does not make sense we are talking about subsets from the same vector space you cannot compare apples and oranges right. So, this said I mean you can just add maybe 3 apples to this I do not even know how to take their linear combinations unless I have all the objects coming from the same vector space. So, 1 x 2 x 7 x 3 x squared 5 x squared and 5 apples that is not a vector space right yeah yeah yes yes both of them must be from the same vector space only then we can compare this property of linear independence and dependence and this subset relation and so on right. So, we will now introduce the second important concept for today's lecture which is that of generating. So, what is the generating set once again at the back of our minds we should always do well to remember that there is a vector space that we have in mind everything that comes does come from that same vector space nothing is outside of that structure okay. So, suppose G this is a subset or a set sitting inside the vector space V. So, this is the vector space this is a set okay let us you know subset is a given. So, you just read it as a set there is a set that is contained in the vector space V. So, every element in this set G belongs to the vector space V is what I mean by this right such that the span of G is equal to V okay that means by combining fellows that are contained inside this set G I can cook up every vector that lives inside this vector space V okay. So, if I have such a set right then G is a generating set for V do you think that the generating set needs to be unique once again think of the polynomial I love to give the example of the polynomial because that is the first like you know simple example that you can give and yet it is not something that looks like an n-touple at least not at first glance later on we shall see when we assign coordinates they are also like those n-touples of numbers but nonetheless the point being that once again you see 1 x x squared you are using these vectors you can generate every polynomial of degree 2 or less by the same token you can also take a 5 7 x 8 x 3 x squared plus 2 4 x squared this is also a generating set you can check right this is also a generating set for every polynomial of degree 2 or less okay. So, of course, there is no question of having a unique or degenerating set okay it is I can all at best be a generating set for a vector space yeah that is why we do not talk about the generating set for a given vector space once you come up with one generating set we are happy with that. So, these are examples yeah so these are generating set this is g 1 and this is g 2 of course the vector space we have in mind is again that same right so that is the idea of a generating set if by combining fellows inside a given set you can cook up every possible vector that lives inside the vector space it is a generating set for the aforesaid vector space right but now we are going to try and trim it. So, how do we trim this generating set we introduce the idea of a basis. So, now we have the ideas of linear independence and of a generating set and we combine them to define what is a basis for a vector space okay set B contain inside the vector space V is said to be a basis for V if it is a linearly independent generating set for V see none of those terms we have used now are not are undefined we have defined what is linear independence we have defined what a generating set is. So, based on our understanding of these two notions that is all we need in order to understand what a basis is right. So, let us look at a few examples just to make things clearer. So, example one let us say the one we understand very well Rn n tuples of real numbers over R of course and I put it to you that this bunch of vectors is a basis. How will you try and establish this well it has to have two properties you take any n tuple of numbers it should be representable as a linear combination of these fellows. So, without loss of generality choose alpha 1 alpha 2 alpha 3 till alpha n you will see that it can be written as alpha 1 times the first one plus alpha 2 times the second one plus alpha 3 times the third one plus so on and so forth till alpha n times the last one. So, it is definitely a generating set then the next thing to check is whether this is also linearly independent suppose it is not when you choose c 1 times the first one plus c 2 times the second one plus c 3 times the third one so on till c n times the last one equate that to the 0 vector in our n tuples that is all 0s. Now of course, entry wise you have to compare if two vectors are equal if two n tuples are equal then every 1 1 to 1 entry should be equal. So, therefore, c 1 is equal to 0 c 2 is equal to 0 and so on likewise all the c i's must be equal to 0 and therefore, nothing but the trivial linear combination of these fellows can lead to the 0 n tuple and therefore, this is also linearly independent. So, this is indeed a basis let us look at example 2 which is c n over c once again the same b is still a basis go ahead and check you can have n tuples of complex numbers and you can combine them linearly over the field of complex numbers. So, every one of those n tuples is a complex number. So, you are free to choose those coefficients instead of real they can now be complex. So, again by the same token it has to be linearly independent and generating set again checking generating set whether the fact that this is indeed a generating set for this vector space over c that is also readily evident the fact that this is linearly independent is also follows the same line of reasoning as presented before. But now if I tweak this a bit let us I should say n because this is probably a non-example let us say c n over r that is also a legitimate vector space right the field has changed the set v has remain the same. Now, do you think b now b is candidature is under question why is it still not linearly independent well of course, it is it is still linearly independent just go ahead and take linear combinations of fellows in b over the real field we have already seen as linearly independent. So, why does it fail the span? So, what do you need to do in order to actually cook up a generating set for because it is a generating part where this has failed not the linear independence part. So, can you fix this right? So, let me call that give that a new sort of a nomenclament notation like this and then I take the union of b and i b. Now, this does not remain a non-example anymore now it becomes an example of a basis yeah. So, see that is why the field is very important the vector space can only be studied and it is structured understood in entirety only once we know what field we are looking for right. So, same c n over c and c n over r the basis what remains a basis in this fails to remain a basis in this right. So, these are important notions of course you can go ahead and check that polynomial the vector space of polynomials of degree 2 or less you can go ahead and check that 1 x and x squared is also a basis for that yeah. The fact that it is a spanning or a generating set is obvious just whatever the coefficients of your polynomial just go ahead and put them as c 0 times 1 plus c 1 times x plus c 2 times x square and you have all possible values of c 0 c 1 c 2 covering all possible polynomials of degree 2 or less yeah. So, thus generating part is done the linear independence we already spoken of in general you can take polynomials of degree n or less and check that 1 x x squared x cubed till x to the n they do indeed provide you with a basis for polynomials of degree n or less right. So, that we have with that we have understood two the three fundamental notions and how they are tied together the idea of linear independence the idea of a generating set and now the idea of a basis these are very intimately connected with each other right and we have also seen a few examples I am sure you will find a lot more examples not just in the textbooks, but also in the problem sheets that we shall be subsequently sending out ok. Any questions thus far? Oh I B is basically I am just going to replace the once here with I that is the square root of minus 1 the imaginary number it is just a name that I am giving it is not something sacrosanct that you will find in textbooks it is just I am defining for my purpose of or my ease ok. So, every element in the set B being so called multiplied with the imaginary I am calling that set as I B it is just my nomenclature ok you can even say maybe it is non-standard, but that is the way it is like we have the argon plane we say R and J R in electrical engineering we use J for the square root of minus 1 right. So, J R is the imaginary axis. So, I am just saying B and I B right this is union yeah no, but these are sets these are not vector spaces B and I B are not vector spaces these are sets. So, we are we have only spoken about sums of subspaces remember not sums of sets right ok. Any further questions otherwise we will bring this module to a close and we will move over to the next ok yeah C n over R yeah all the all the scalar R's can come from the set R yeah yeah no, but I B is the set of vectors. So, members of B are first coming from C n. So, members of I B are also coming from C n. So, they are obviously n tuples of complex numbers. So, I is a legitimate complex number with specifically 0 real part and 1 imaginary part. So, those are definitely members of C n it is only the scalars that you are now restricted to choose from only the real numbers not complex numbers. So, just that restriction includes I mean entails that you will now have to choose twice the size of the basis twice the number of elements that you had in the original basis in the this basis yeah ok.


Earth's ozone layer is on track to fully recover within decades, as ozone-depleting substances are phased out around the world. Like many countries, St. Lucia has advanced its phase-out of hydrochlorofluorocarbons, or HCFCs, and ozone-depleting substance that is commonly used in foam, refrigeration, and air-conditioning sectors that destroy the protective ozone layer and contribute to climate change. Keisha Jabatist from the National Ozone Unit outlines the activities scheduled under the second stage of the HCFC phase-out in St. Lucia. We're launching the second stage of St. Lucia's HPMP. It's our HCFC hydrochlorofluorocarbons phase-out management plan. And this plan outlines our overall strategy to phase out HCFCs by 2030. Sulton, who prepared our HPMP, will be presenting the key elements of the plan, which include capacity-building activities for refrigeration and air-conditioning technicians, updating and strengthening our legislations to control the import and use of ozone-depleting substances, especially HCFCs, our plan to enroll education and awareness programs so that consumers and the general public will be aware of the HCFC phase-out and what alternatives are out there that are better for the environment and more energy efficient, and also the plan to establish a reclamation facility for St. Lucia in order to encourage the reuse and recovery of refrigerants. St. Lucia's HCFC phase-out is funded by the Multilateral Fund to the Montreal Protocol, an international treaty designed to protect the ozone layer by phasing out the production of numerous substances responsible for ozone depletion. St. Lucia met obligations to reduce consumption of HCFC by 35% on January 1, 2020, and accelerated the phase-out of chlorofluorocarbons, or CFCs, by 2008, two years ahead of the Montreal Protocol schedule. According to data, St. Lucia is on course to complete HCFC phase-out well ahead of the 2030 schedule. In his address at the Stage 2 launch, Mr. Leslie Smith, refrigeration and air conditioning standards expert from Grenada, commended St. Lucia for its phase-out achievements and caution stakeholders for the work ahead. We must never become complacent until we are assured that the ozone layer is finally recovered. In doing so, the launch of the Stage 2 HPMP signifies the government of St. Lucia's commitment in contributing to the global effort to preserve, protect and enhance our fragile environment. While this project addresses ozone depletion substances, you must be mindful that the replacement technologies do not introduce greenhouse gases that would make it difficult for you to achieve the targets under the Kigali Amendment. And therefore, you are encouraged to leapfrog these high global warming potential alternatives and to move into a more sustainable and long-term solution. The Kigali Amendment to the Montreal Protocol aims to reduce hydrofluorocarbons, or HFCs. They were developed to replace ozone-damaging CFCs and HCFCs, but they have high global warming potential. The official launching ceremony for St. Lucia's second stage of its HFC phase-out management plan, held on 9th February at the Bay Gardens Hotel, was attended by stakeholders of the refrigeration and air-conditioning sector, officials from customs and excise department, the Ministry of Commerce, the National Air Conditioning and Refrigeration Association, and retailers of equipment and refrigerants. For the Department of Sustainable Development, I am Jesse Layance reporting.


Hi and welcome to School Puzzle, I'm your host Sarah and this is the show where we chat with everyday entrepreneurs about everything that goes into starting a new venture. Today's guest has made strides in pushing the boundaries of the sexual wellness industry. Eva Goykoche has started Lawn in 2018 after feeling frustrated with how outdated the family planning aisle had consistently become wherever she went. So she decided to converge her work experience and create a modern sexual wellness company that is built on quality, simplicity and inclusivity and her goal is to make intimacy better for all people. Welcome Eva, it is great to have you on the show. Thank you, it's good to be here. It's wonderful to be in your beautiful apartment. Thank you. I mean this is plexiglass. I am with our jail cell plexiglass. So Eva I've heard a lot about your company. I've investigated a lot. I've checked out some of the products. I would love to hear your story of why you decided to start this. Yeah I mean so without totally revealing my age I have been working for a very long time. I was a legislative aid in healthcare in my early 20s. I study marketing in New York actually so this is the second time I've lived in New York and I started working in marketing after I left politics and started working for a lot of startups and with really cool brands and my interest was like how can I work for a company that converges healthcare and sort of this startup consumer friendly facing brand and sexual wellness is extremely outdated. The same brands 100 years it's like it's so true. It's so boring on the aisle and I thought that this was something that for me made such an impact on many levels that that I decided to pursue it. I did not think that like it was an idea and then all of a sudden here we are but now here we are only two years later. Well I started working on 2015 but we launched in 2018. But still that's a huge success story and today you have many employees you sell in how many stores do you sell in? I think we're in like 140 stores but we're mostly D to C so we're mostly a consumer. Right because people can go to your site and buy all the goods there. Now with sexual wellness I feel like there's a lot of experimenting involved in that and what you exactly want to make, how to make it, the products. What's that process like because I imagine there's there's a lot of certifications you may need. There's a lot of experimenting you may need with different products to figure out what really needs to be updated. Yeah so the idea was launch with the basics and create a brand that matters to people with the basics. Okay so you you created the all of the different products. Now tell me about the process of of bringing that actually to market right? So like how do you market something like this? How do you stand out from other people? I mean the idea was first of all we did a really big survey to sort of test if this was even something that people wanted. Yeah and which is so good by the way. Yeah there was a lot of interesting feedback. Yeah and a lot of it was the same like people everywhere from 18 to 80 were in this survey men and women other, gay straight other and they all said the same thing which is like current brands are they're really explicit they're really misogynistic they're really outdated the packaging is just like so I thought look this is a viable idea and it's also a really emotional category so if you can create something that really matters to a person and you're creating these like really great basics you can sort of build a company off of it and the way that we differentiate ourselves by having that emotional connection and that brand equity. Yeah and I think I noticed that when I look at your social media and your marketing strategy you use the word misogynistic for other companies some companies right and that's actually one of the things that I was really inspired by how you kind of do put women first in many situations and it's like women are powerful and that is such a great thing to see in this industry because it's not something you normally see and and you know it's an outdated mindset. It's an outdated mindset and even like the joke around family planning I mean we put that on the site to sort of say it's called family planning like this is yeah we're in 2020 and I know we feel a little like we're going backwards but but I will say like we are gender inclusive our audience is almost split to the site and a lot of people are in relationships so we're really getting to both genders and then we're also inclusive of the gender spectrum because that's not something that really gets talked about. Right and that's on the site too by the way like that's one of the things that pop out and that also is not addressed in other sexual wellness companies. No they're really gendered and this idea it's not we always make like the common it's not about being so forward thinking in that the product isn't for a specific you know they are male condoms they are you know obviously yes but the idea is like sex and gender aren't always correlated. Totally so and your products actually speaking to that a lot of sexual wellness companies it'll be like a pink thing for a girl and a blue thing for a boy. Years are not like that. Years are very they look very luxurious. Tell me about designing packaging because that's a big part of branding as well is designing your logo designing the packaging how do you how did you start that. So it's interesting because Maud has gone through multiple lives yeah like when I first started it was blue it was like really blue um and the idea was for it to stand out on the shelf and as we started going through this process of like what do we really stand for I think the packaging started to become the thing that really cuts through the noise yeah by being neutral so many lives later we worked with the designer to create the symbols and then we worked with other designers who we still work with to create the packaging and but we basically do everything in-house like hand-in-hand with those people it's not like we worked with an agency to go through the whole process I created the brand book that's where I come from um so your professional career helped you launch this in what ways did that career help prepare you for a career in entrepreneurship well so it's funny I ended up getting my degree in organizational communication which I didn't I knew it mattered I care about how you know the structure of companies and sort of the communication and culture building but I didn't realize how much this would come into play later yeah and then understanding like healthcare policy and how you navigate your own wellness and so those things were really foundational and then I went on to help people build brands and I was like a really employed ever lane and I worked for an organic cosmetic company and so this marrying of product and like really what those products mean in someone's life especially when it's about wellness and health yeah um was what prepared me for this so why did you want to become an entrepreneur and take on all of that because in many ways it is easier working for someone else but it's so much more enjoyable working for yourself yeah I mean I think if I saw a company like mod in the world I would have gone to work there because when I left everlane the idea was like go work for a company that you believe in yeah um I believed in everlane but it was like I don't care about clothing I care about health and so uh I built a company I wanted to work for and like I enjoy being an entrepreneur and it's it's about people and some some days you feel like you want to throw your hands up and be like I don't know I'm also a person I think this idea of doing something that really matters that I could wake up every single day and do and I know that's super cliche to say like was what I wanted yeah and so I completely understand yeah once you have something you're so passionate about you can't even imagine going back and working for someone else and then that's the beauty of running your own business yeah yeah so why call it mod so mod was this play on modern uh mod means strength and battle it uh it also was kind of a nod to the show mod which was really it pushed the boundary at the time for reproductive rights yes and then also the real backstory is that I won't go into it too much but there was a prohibition era for condoms and all of this beautiful packaging came out of that time because they were trying to stay under the radar and there was a brand that wasn't by any means like the prettiest of the bunch but it was called three merry widows and if you open the packaging they're married windows three merry and their names are agnes becky and mabel and I was like I feel like mod would have been the fourth widow yeah totally it was all of those things launching your own business can be very expensive so how did you get the funding to launch something like this something question I know it's often the hardest part it was really hard yeah I I moved to New York for mod like I wanted to build mod I was ready I sold my house in LA I moved for mod and the idea was to start fundraising and build out network but I came really with no network to do that and um and it just started with one conversation that led to another and in 2017 I raised my first round of funding it was going to be 250,000 and we raised 550,000 wow congrats it's congrats but it also is incredibly like when you're talk full it's stressful but it's also if that's not the math you anticipated then yeah you are really diluting yourself so right um yeah tell me about that funding um it it's can be very overwhelming for people so where do you get it to like who do you talk to what do you do to make sure you're using the money in the right ways once you get it yeah I mean so for me there was a couple things that I did that really helps with the tone um the first one is I joined like an accelerator in the summer it wasn't an accelerator that takes equity which was good so I was just able to be around other entrepreneurs and ask a lot of questions when you say an accelerator what exactly is that an accelerator is usually a program um that will incubate a startup and give you access to an office or access to capital sometimes they take a percentage of the company um sort of to give you the tools you need to launch what were you feeling during this time well so it's interesting the night that we launched it was April 2nd 2018 and I stayed up all night with the developer I walked outside and there was snow on the ground with daffodils growing oh and so like permanently imprinted in my brain that I know was amazing um so there were a lot of sleepless nights I also really wanted to be committed to as typical as it sounds like a work-life balance and making sure that I wasn't just work because at some point in the middle of the night like your brain shuts off there's no way that you're useful anymore thinking constantly yeah yeah and you need to rest your body you need to rest your brain totally so we have good work-life balance now um we go home at 6 30 which is kind of unheard of in startup land and in new york yeah that's true but I think that ability to sort of maintain balance also goes back to the ethos of the company which is to make time for intimacy so what would you say is the most shocking thing about the sexual wellness industry that people don't normally expect I think one is they don't realize how few brands there are like really Trojan own 70 percent of the market no way yeah there are many in many you probably haven't heard of but really there are three major condom companies that everyone knows so it's Trojan directs and lifestyles okay yeah it's been totally owned by brands in a way that actually has this trickle down effect to how people feel about themselves essentially right and we compartmentalize it and we're uncomfortable and we don't have these conversations around the dinner table and I think like you know the point for us was to really create a brand that could be like a dinner table conversation you can talk to your teenager about sex you can talk to your partner you can be over 50 and not feel like suddenly you know sex isn't something that you should think about and I think that that's like mods really trying to yes we're a product company but we're also really trying to shift culture and communication and so what has been the most surprising thing that's happened in running your business so far oh god what's the most surprising thing I mean I think it's that if if things can go wrong they'll go wrong yeah you're like we have this supply chain figure that world COVID COVID it's a good one um yeah no I think like supply chain and just making sure that you like really cross your t's and dot your eyes and even then it doesn't ensure that everything's gonna go perfectly well so being resilient not taking it so seriously just being a malleable like person who can sort of go along with the stuff that's gonna take the punches and go um because failing is part of entrepreneurship and you just learn from failure move on if you get stuck on it that's when things don't do anything because you're stuck on it yeah and I think like when people want to raise money I always want to ask questions around like personally are they prepared because it is a lot of rejection I mean it's like being an entertainment like there's a ton of rejection so much rejection it's easy to maybe take personally um and so you kind of have to be ready to just be told no and you have to be able to have a very thick skin too and I think a lot of people need to understand that before they decide to start their business it's normally what weeds out people that won't succeed very quickly it's just is the the constant rejection I mean it's it's you get rejected more than you you get successful totally uh so it's like what would you say is the best way to deal with that as someone that isn't used to that rejection but still wants to start their own business and needs to get used to it I think I know I think there's a lot of myopia around like you think it's a good idea that doesn't mean that everybody else thinks it's a good idea and it's okay if they don't because if they thought it was a good idea it probably already somebody already came up with it right so that's one is like understanding that not everyone's gonna like your idea but also understanding who's the right fit to go to for funding who's the right fit it's like dating like who's the right fit to go to for funding and who's and are they gonna like you like put it get yourself outside of your your own head and say like is this the right match is this gonna be a reciprocal relationship so did you have an idea for mod and then after the survey you realize actually I think we should do a little bit differently in this direction or was what you had envisioned pretty much what the survey also told you it was what the survey also told us but I think that what I was saying earlier about going through iterations on the brand that was there were a lot of decisions that had to be made around like okay well the second version of mod was really colorful and that's sort of impossible to get to market because it's very expensive and then expensive because if you're printing all of these different colors if you're doing all of these different runs like it's so and then we realize well look if the if the whole thing is to be really universal and this company that stands for all people like color does matter yeah and maybe it's not in showing every color that's gonna bring them into the whole maybe it's in being more simple so those things were happening sort of at the same time the other thing I was gonna say is business model like unit economics which nobody really yeah tell me about stay here not a very exciting topic but it's a super important topic it's an important topic because not every company should fundraise because they don't have the unit economics to do it um or the business model to do it so it's like okay so now you have a thick skin you think it's a good idea yeah is it actually a good idea on paper yeah is the math there right and that's really important actually speaking of which was there an aha moment for you there was not was it so between leaving everlane and I started working for for other brands like I was I was helping them build their brands get their websites off the ground and I worked with this designer duo we started this little wash company it was great it still kind of exists um and they started talking about sexual wellness and I was like oh my god this is the idea I've been waiting my entire career for because this matters so much to me yeah I come from a state that's 48 like on the list of usage for condoms I have you know there are many teenage pregnancies in my family um and so for me it was this really like well moment of I want to do this do you want to do this and not everybody was on board no you know not everybody wanted to sell condoms and tell their grandma that's what they did my very catholic grandma is now okay with it but took a while um so yeah if there was a light bulb moment and it was a conversation and it was at the time it seems like so far out of reach and so impossible that it just was a conversation yep and that's normally where it starts yeah do you have any advice for aspiring entrepreneurs yeah I mean do your homework and yeah and you know maybe you don't want to take the Harvard course but there are definitely like courses online they're Coursera is a good resource there's like other resources where you can start to learn more about what you're building and google it I go great you can learn so much on youtube these days how long it took to get off the ground was really my it was the time learning it was a time educating myself and getting told no and being poor for a long time well I still don't make much money that's another big like money just so you know you're not going to make a lot of money if you're a startup founder yeah I'm going to do a little household with the husband of 10 years thank you Ian for like helping us pay the rent yeah I mean every once you finally get there and you achieve your dreams of this company every um every tier you shed every challenge every second second guess it's all worth it because there's nothing like being so pleased with what you built so it's been wonderful having you on the show Eva thank you so much for joining us and thank you to everyone out there who tuned in today and you want to learn more about mod visit get mod calm follow them on instagram and get mod and that is all for this edition of school puzzle you can keep up with all of our episodes on youtube apple podcast google podcast or whatever you screen and download podcast and if you do like what you hear today please consider leaving a review share it with your friends and subscribe to our show we'll see you next time bye


Epidural blood patch, EBP, is a procedure used to treat certain types of headaches caused by low cerebral spinal fluid pressure. It involves injecting one's own blood into the epidural space to stop leaking of cerebral spinal fluid and prevent further damage. The procedure has been shown to be effective in treating post-dural puncture headache, PDPH, and spontaneous intracranial hypotension, SIH. However, there are some risks involved, including increased intracranial pressure and rare but serious complications. Proper planning and monitoring during the procedure is important to ensure safety. Additionally, EBP should be considered in patients with COVID-19 since it can help reduce the risk of developing complications related to low cerebral spinal fluid pressure.