The following is a presentation of TFNN. The Trader's Edge with Steve Rhodes. Toll free at 1-877-927-6648, or internationally at<PHONE_NUMBER>. The Trader's Edge. Now, Steve Rhodes. Good afternoon, folks. Welcome to what today is October the 17th. This would be the terrific Thursday edition of today's Trader's Edge. I'm your host, Steve Perseverance Rhodes. I want to thank you all for being here. And hey, this next 60 minutes, it's all about you. So give us a call at<PHONE_NUMBER>. We'd love to take a look at whatever instrument it is, whatever timeframe it is that you've got interest in. Maybe part of your portfolio. You're looking to get into your portfolio. If you can't give us a call, you can always send me an email. Steve at TFNN.com inside the subject heading. If you'd be kind enough to put radio show question, of course, in our Tiger's Den. And in all, Pings will do. So let's go ahead and get this show started on terrific Thursday. Of course, this is Tiger Financial News Network. Again, I'm Steve Rhodes. Welcome to the show. Right now, all the indices with the exception of the spot ball, I'm sorry, with the exception of the socks are in the green, albeit slightly. Although the Russell 2000 having a strong showing, as well as the transports, they've built up eight to nine tenths of a percent to the upside spot ball. Tilted X is actually ticking a bit higher. It's up 20 cents as we speak. Gold's up four. Silver's up a little over 1% 19 cents. C-straight now at 1762. Light sweet crude back 15 cents. No big deal there. Natural gas pretty much flat. Same as a treasury bonds are up eight ticks out there. Lead the charge to the upside. It's a ticker symbol F D US G. Fight us. Investment Corp. Boston beer is up $19. That one was up 24. Maybe it's a IPO.  It's up 2400%. It's a good day. There's no doubt about that. You've got pool corporation up 9%. About $19 Amazon 14 to the upside to the downside. You've got Provident Bank Corp off 11 bucks. Well, 51%. That's a haircut. IBM is off 9. M&T bank down 7. Beyond meat, which is beyond me is off $5 and 50 cents out there. You won't get Stevie's son. Hey, I like my fruits and vegetables, but that means I like my fruits and vegetables. And I like my hamburgers. I don't want to mix them. Anyways, that's neither here nor there. Look, let's go to our first question out here.  I'm considering a long position with a close above 190 90 target around 205. So what are the charts communicating to us? So let's go take a look at Facebook here. Andy are the three different Andrew. I apologize. And let's be more correct and formal out here. If we take a look at the daily, the weekly and the monthly set of profiles prices above the daily resistance, which perhaps may be support 180 206 prices trading within its weekly set of profiles. So support there would be 184.75. This is a bullish structured profile, which would say you were looking for a close above 190. In this case here, this would say, hey, a close above 194.31, not 194.32, but you know, caught 195 and above, which suggests to move to the 208 area. You're looking for move to 205. So this has got 208, but the monthly chart, its profile shows resistance at about 200. We're trading at 189.56. Okay. So there's our profiles weekly and monthly prices trading in between the support and resistance areas. If we take a look at, and you're looking for an entry point. So if we take a look at Facebook, we take a look at the daily timeframe, what you would have liked to have done is to have inquired about Facebook on October 3rd. The reason is, if we take a look at the daily chart for Facebook, both it's high. And when I refer to the high, I'm referring back to the July 25th high. And then the low, the low being the October 2nd low, were both formed with rose momentum indicator signals. This is the way that markets like to, they don't always. It's just when you do see these patterns present, this is how markets signal to you and I that it's forming bottoms. So your actual entry into Facebook was October 3rd, October 4th, October 7th, October 8th. And it's not going to be on October 17th. And I can't see trading, waiting for this to get to 19090 out here, your 18953, but you've got to make the reward risk scenario. It does appear that using just Stevie's white background charts with these tools out here, that what price is gunning for is 20288. You can see though, in the area that price book is trading right now, and I'll use the high, just kind of check on the high of September 20th. That level is 19310. And you wanted to close above 19090. See, that's a three river evening star pattern out there. So we know where sellers are present, because in the same area, two different times, you had a nice little dark cloud cover on September 12th, a nice little bear sash on September 6th. So Facebook really in order to give you the signal, the coast is clear to make the rise to 20288, irrespective of what we looked at on the weekly, and the monthly set of profiles. You've got to clear resistance, which is going to be the high from September 20th. So the better pattern, the better entry would have been down there in that early part of October versus now on October the 17th. And if we look at the weekly timeframe chart, it would say even if you did go along back on the third or the fourth, price is now running into its resistance level, its potential of a counter trend resistance level. That is Stevie's green line. Price is trading at it right now. So obviously if you can close above this on a weekly basis, and then as well as the three river evening star resistance level, that would suggest the move higher. Now, in this case on the weekly, if in fact all that comes to fruition, it could give you a price target of $218.62. But when we look at the weekly chart, Andrew, price is up at resistance. The daily showed us resistance over on the left-hand side of it in this price range. And if we look at the monthly chart, we can also see that price is up at resistance. Stevie's green line. So my preference for you, you've got to make the decision out here. I've given you all the numbers, so you can do the risk reward out there. But right now you're at resistance, so you just keep those hands in your pocket out there. And I'd rather you take a look at Facebook when it made its high out here. This is back in July on a monthly timeframe, with the roads momentum indicator pattern out there.  Maybe you are a subscriber, I don't know. So we've got the archived videos to assist you with that. If you're not a subscriber, just consider doing that for at least the next 30 days, because you can cancel it. And then you'll get the education that will assist you in being able to identify those trades and where it is that you could enter Facebook out there. So Andrew, thanks for writing in. I don't recall getting a question from you before if I did, my apology, but thanks for taking the time to write. And folks, I want to hear from you as well. We've got Phil. Phil writes in and he wants to go get a burger, as a matter of fact. Now I haven't been to this place out here. I don't know if they sell those impossible burgers or whatever they call, but if we take a look at Shake Shack and the ticker symbol is S-H-A-K. Now maybe it isn't a burger that Phil wants. Maybe he just wants a good old shake. I've got to assume they sell shakes out there. Now, when I was a young kid, well, so I took a hockey puck. I was playing. I was a fairly good hockey player as a young kid. I was playing with the older guys five, six years older than I was. Didn't have face masks at those time. And I, in my mouth, stopped a goal from going in. I was in front of the goalie and simply took the puck into the mouth. Lost my teeth. Lost my front teeth. Lost a bone up in my nose area. And then eventually had to have 12 teeth pulled from my mouth. I lived on shakes for a long time.   But we come back from this. It doesn't matter whether I like shakes or not. We're going to go take a look at Shake Shack. This is a standalone piece of software that instantly filters over 2,500 global financial markets such as stocks, ETFs, commodity futures, and forex. Heated by Steve Dahl, Taz understands that in today's technological world, the use of top flight software applications and technical analysis expertise is essential to successful trading in today's market. You also gain access to the webinar that Steve Dahl and Tom O'Brien just hosted. The best way to use the Taz Profile Scanner to profit this webinar archive is available for all subscribers immediately upon signing up. All new subscriptions also come with a 30-day money-back guarantee so you have nothing to risk. Start your subscription by visiting the front page of TFNN.com today and you'll find the Taz Profile Scanner under the Services tab. Sign up today. Are you in the market for buying or selling real estate in the Bay Area including the surrounding St. Petersburg, Tampa, and Clearwater markets? Tiger Real Estate LLC is a firm that has extensive experience in the Tampa Bay Area. Whether you're looking to sell your current property for maximum value or you're in the market for a second home or investment property, Tiger Realty has the experience across all areas of real estate in the Tampa Bay Area to help buyers and sellers make the most informed decisions across all price levels. 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Details on the Tiger's Den are on the front page of TFNN.com. TFNN has launched our brand new website. You can still visit us at the same TFNN.com URL but when you do, you'll see a new and improved homepage with a much simpler navigation, whether you're watching Tiger TV live in high definition or just accessing your newsletter subscriptions. We even have new pricing in six months and yearly options. Check out the new TFNN.com now and experience all the upgrades. TFNN.com educating investors. All now toll free at 1-877-927-6648 internationally at<PHONE_NUMBER>. Let's go to take a look at the Shake Shack out here. Phil writes, and just bought Shake as a TD9 setup. Where would you place your target? Market profiles and so on and so forth. So, Phil, if we take a look at market profiles, let's just begin their daily, weekly and monthly. Here's what we know about Shake Shack. Today is trying to get inside of its daily profile. So, you'd really love to see a close above 9229. That is the bottom of the box. The reason is because if Shake Shack does not close above that, it's just a clear level of resistance, old support that now is resistant. So, 9229 is your key level to be watching today. It just so happens on the weekly timeframe, the bottom of its box is 9247. So, certainly if you saw a close below 9247, from a profile perspective, that would not be good news. On a monthly basis, the profiles really don't come into play for you and I. If we look at the daily timeframe chart, and today could be, could be day 9 of a TD set up 9 count. But as we speak right now, it's not. And here's the reason why, Phil. First of all, in order, so today is day 9. Yesterday it was bar number 8, or bar number 8. Well, today, because we're looking at a daily chart, but bar number 9. And in order for bar number 9 to actually form, therefore give you the TD set up 9 count, today's close must be below the close of bar number 5, the bar 4 bars earlier. So kind of easy math out there. And if you take a look at bar number 5, price is trading above it right now. And the close of that was 9162.  Doesn't mean that this might not bottom, but this is not a valid, what I'll call a valid, it's a, oh, how do I say this? This is a, well, right now it's not a valid TD 9 count because it's not going to form based on where price is trading today. So we gave you that number where price must close below. But even if it did, let's assume that price did close below the close of bar number 5. Bar number 6, Phil, is the candle that has lowest low of this pattern out there. For Stevie, right now at this stage of the game until I get all my software ducks in a row, so to speak, it wouldn't be a tradable 9 count pattern for me out there. So that's the daily, that's what I see out there. You were asking where would be the target. So targets, you've got the profiles. We didn't talk about those. So on a daily basis, the target would be 9866 or 10121 to the upside. And if price close above the bottom of the box, that still may be in play out here. In order for that to happen, you're going to need to see a close above Stevie's green line eventually. That's 94 bucks, even Stephen. So that's what I see when I take a look at the daily timeframe chart for Shake Shack out there. And then 10376 is where we have a TD setup breakdown, the most recent one, but there could be a new one depending on where the close is today because the new one would be the high of bar number at this stage here, bar number one, which would be 9457. So that's the daily charts for Shake Shack. A quick peek at the weekly for you to see out here. If there's anything, there's nothing on the weekly price below Stevie's green line out there. Let's just do a wave count. See if this thing got to wave number seven. I'll be a monkey's uncle. Where did I'll be a monkey's uncle came from? Or am I just imagining that? So here we go. We just took a look at the wave counts by starting from the low out here from December 28th. And Phil, this made wave number seven on the week of September the sixth. It have had a couple of bearish reversal candles priced below Stevie's green line. If we were just looking at this chart, this would suggest to you and I that Shake Shack is gunning for 5815. So this would say be careful out there now because we saw that we've got to go look at the monthly chart, see what its signals are. As we look at the monthly chart, well, this appears to be a TD setup, nine count top on a monthly time frame chart. Now the last time that Shake Shack made a monthly TD setup nine count, it was right here. The month was June of 2018. And of course price then moved lower for the next about half of a year out there, six months. So this is not a good thing because right now it looks like the close on a monthly base is going to be well above the close of bar number five. So you're going to get another TD set. You're going to get a TD setup nine count on a monthly base. So I just simply offer caution to you based upon the patterns that we just looked at on the charts out there. But best of luck with that trade out there. Let's see, do we have any other requests? We do. LB writes in and thanks. And some folks wrote in yesterday and it was late in the show. So I just urge you to please get your request in early, preferably not at seven or eight or nine in the morning. Makes a little bit, you know, before the show, just before the show would be great out there. Then I promise to get to your request. So GBTC again, we were talking about this, Lee had written in, I think yesterday, the day before, what have you about, this is Bitcoin trust out here, GBTC. And it indicated it looked like it could be bottoming. So the problem I think is we just see if I've got any way to pull up the, to pull up Bitcoin on my other charts that would at least assist us with what it's doing. That didn't work really well. So that's not going to work. At one point, Nan, and the other thing I've got to pull up on my own. So bummer there. And it's trying to do that. GBTC, GBTC, the, so I'm just going to go back to the, going to go back to the ETF itself. So we're just going to trade based upon the ETF. Now what you'd like to see here, so today, so far, Lee, is today as an inside bar, inside candle. See today, the body of today's candle is trading with inside the body of yesterday's candle. And yesterday was a gap to the downside. Now I recognize a price in these gaps here is just catching up to what's going on in Bitcoin overnight or I assume that that's what it's doing out here. And so you've got resistance at the low of October 16th of 926. And you don't have a bullish reversal candle. You do have price moving lower, doing less relative energy, but you do not have a bullish reversal candle. It doesn't mean that yesterday wasn't the low, it just doesn't fit the criteria that I use for the pattern that I created here with regard to that road momentum indicator. And that's what we really want is, you know, I can do enough studies to prove to myself and hopefully over time I have proved to you too. Markets are going to, I don't care what pattern it is that you and I trade, it doesn't matter what pattern it is. If price is moving higher, it's going to continue moving higher until at a minimum you see some type of bearish reversal candle. Likewise, if price is moving lower, no matter what pattern is in place, it's going to continue moving lower until the cavalry says, I'm willing to take a stand.  We don't have the, we don't have that signal here in GBTC for its daily timeframe out here. If I look at the weekly timeframe, weekly timeframe says this is going to be bar number eight on a weekly base of TD set up nine count, but it also says, you know, price could pull back to 448. So weekly says, hey, maybe you're getting close to the low of bar eight or nine or the bar following nine can be the low of that pattern. So we don't, you need, you need next week's candle before we can even make that determination. And on a monthly timeframe out here, nothing for us to really pay attention to. Now in the futures marketplace, we're about to go to break out here. And so I was just going to try to see if I could BTC Z nine. Let me see if I can pull up anything else to assist Lee with his GBTC trade. We'll be right back. I'm certain you are or strive to be one of the best of the best at everything you do in life. It's the most common trade that we tigers and tigers share. If you're looking to become the best of the best when it comes to managing your money, let me teach you to do what most wealth managers tell you can't be done, which is how to time the markets. I'm Steve Rhodes, author of Mastering Probability. And for the last 12 months, Timer Digest has been tracking my newsletter signals, which have earned me the ranking as their number one market timer in the nation for the S&P 500 for the last 12, 6 and 3 months. Timer Digest also ranks me as the number one market timer for gold as well. The fact is markets can be timed and I'll teach you the exact set of tools that I use that has transformed me into one of the best at what I do. Sign up for Mastering Probability today by clicking on the newsletter tab on the homepage of TFNN.com and get immediate access to workshops where I take you step by step how to use an extraordinary set of tools as well as provide great market calls too. Sign up today. 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We are so confident that you're going to love this new charting software that will even give you a 30 day unconditional money back guarantee. Don't miss out on this incredible new piece of software. Get your copy of The Art of Timing the Trade Charts today by visiting TFNN.com. All right folks, so let's finish off Bitcoin here. We do have the December futures contract for Bitcoin futures, and I can't pull it up on my other system here, but here's some other levels for you to track. Lee, there is a daily profile, bullish structure daily profile out here. The bottom of it is 8083. Today is not a bullish reversal candle, at least at this stage of the game from a daily standpoint, but today is not a bullish reversal candle. Today is not a bullish reversal candle, at least at this stage of the game from a daily standpoint. But to go ahead, you're in the trade. Just don't let Bitcoin itself, Bitcoin futures close below 8083. It's a bullish structured box out here. If you can get a move above 83.66, that might get you to 92.15 out there. So best of luck with that trade. Thanks for writing in. I hope that this information helps you. I think my gain on TNA today, so long S&P and TQQ, is it okay to take gains and not put new positions on? Of course, it's okay for you to do anything out there, but I think you're looking for maybe some additional guidance out here. And so let's go to the additional guidance steps. So you're out of TNA, and you took the profits there. So congrats there. Let's not spend our time there. You're asking about the S&P and the Qs out here. So first, let's do this for you because let me give you some info that maybe you don't have access to. And when I say that, I'm referring to the market breadth of both of those instruments out here. And so we take a look at that, and I'm looking right now, I've got the NASDAQ 100 up on our screen. I want you to just focus on the dials in the upper right-hand corner. And what those dials are representing, they're each in the green-colored level, which means that there are more constituents inside the NDX100 trading above the profile versus below the profile. So the first place you would at least see a crossover on some type of bearish condition, so to speak, would be on the 60-minute time frame. So as we pull this up, what you can see out here, just on a 60-minute time frame, you got a bullish crossover on October 10th. So nearly a week ago, a week ago, a week ago, out here, you still have those same conditions, 53 constituents above the top, 26 below the bottom. And all that means is the market breadth is so strong, even on a short-term basis, forget about the 240, the daily and the weekly, that the market breadth is strong enough to say, and even though on a 60-minute ES, well, this is the NQ, let me give you the 60-minute NQ out here. So even on the 60-minute NQ, we do have valid topping signals. So I'm not trying to convince you to do one thing or the other. What I want to do is provide you with information. You're an excellent trader. We can see that here, but provide you with the information so that you can make a decision, because the signals that we have are confusing, confusing at best. What do I mean? Well, take a look at one of the patterns you and I help to use identified tops and bottoms. Price movement higher doing less relative energy. That's what we have out here. We don't really have the, when I said we don't really have, we don't have a bearish reversal candle, even though we did have price move lower out here. Now, where was price moving into? That's always the question. In the NQ, I don't really have a good level of support where it was moving into, at least on a 60-minute timeframe, but the reason why price ended up stopping where it did, or at least this is my thinking as to why, and the justification as to why is because of still strong market breadth out there. So no real key levels of support have cracked inside of the NQ out there. And if we look at the NQ and we look at the daily timeframe out here, small body doji candle, today likely to be day five of a TD set up nine count pattern. We don't know that for sure, but all price has to do today is close above the close of bar number one, which right now that looks like that should be accomplished. 78-59 is the level out there. Maybe this is going on to make a TD set up nine count top. That's the last time that it formed a high out here inside the NQ was a TD set up nine count top back in September. So maybe the same pattern is unfolding out here. You've also got an A to B equal CD to the upside. It looks like this. If we draw that pattern out here, what we're going to see is we're today hit the 1 to 1.272 level and it's backed off, okay? No big deal. Maybe price is on its way to 8109. That would be the 1 to 1.618 area. If we look at, let's see here, if we come here, I'll just slide this over, because we'll go take a look at the S&P. If Phil's got the question or you've probably got the question too, certainly I know that Jay is interested. Are there any new profiles out there? And the answer is no. We take a look at the four quadrants of the ES, meaning with regard to your TNA trade or the Russell 2000, looks like it wants to make a run for 1548 or 1541. It was up a point or two higher than where it is right now. So I'm not going to convince you to jump back in, but that's your resistance point out here. The NQ is above resistance. We didn't see a topping pattern inside the daily chart out here. And so the NQ appears to be running and gunning for 8071. So my suggestion to you is that what the market's communicating to you and I at 1.35 in the afternoon is to remain in that position. Now, what do you do if overnight the NQ targets, hits 8071 and sells off? That's the problem with the ETFs that you've got. Not that it's a problem, just that you can't trade. Well, depending on who you trade through, you may be able to actually trade the Qs. But I don't know about TQQQ as one of those. But that's neither here nor there. Right here is the mere fact that all the signals for the NASDAQ 100, the NQ out here, says that it wants higher price. Now if you look at the ESMini, we'll just kind of glide over to it. Price is above the top of its daily profile, 2995. And so Phil, if that's the case, what it is likely targeting, if there's a close above that today, it's likely targeting 3032. Now, if we take a look at the daily chart for the ESMini, you're going to see really the same thing that we looked at in the NQ. Today is likely to be bar number five of a TD9 count. It has not hit the 1 to 1.2728 to be equal CD. That's 3014. But that's likely where price is headed to, maybe even 30, 50, 83 out there. So, and look, I can show you, and here's where the dynamics and the difficulty in really being able to, I like to be able to have conviction when I provide you with information out there. If there's any one outcome that I have when I do this show for you and provide each of you with information, it is to have conviction behind what it is that I say, not willy-nilly, and then be able to go back to the charts to explain what that conviction is. The problem I have with doing that right now for Phil's question is this, is that when I take a look at my Market Analyzer tool, and this is my short-term timeframe Market Analyzer tool, you can see that the first four instruments out here are the equity futures contracts. And when you take a look at one hour, two hour, and five hour, you're going to see top confirmed patterns out there, top signal patterns out here. And all this is the sign of a potential top. But yet when I take a look at Market Breath, which I know will be a lagging indicator, when I take a look at daily profiles, not necessarily a lagging indicator out here, we have conflicting messages. When you have conflicting messages, taking your profits is never a bad thing out there. But even though these short-term signals, price hasn't really done much in any kind of a sell-off. Well, I guess lastly out here would be to watch the Dow Equity Futures contract. It has not been able to clear resistance, resistance being 27.042, but if it does, if it did, then its price target is 27.375. Now look, we're about to go to break out here, but let's look at the Market Breath for the S&P 500. And what you're going to see out here is each of these are also bullish. These, 60-minute, 240, daily and weekly. It says be very cautious in shorting this market right now. We'll be right back. If you're in the CD market and looking for a secure investment, the Target First Mortgage Program may work for you. The security for these first mortgages are building lots in the Tax Opportunity Zone in St. Petersburg, Florida. The Tax Act of 2018 set up tax-free zones across the country where you can build and hold for 10 years and pay no tax on the profits, which makes these lots valuable. Investment is anywhere from 30,000 to 75,000. The interest paid is 7% yearly paid on a monthly basis. According to bankrate.com, the best rate for a four-year CD in the country as of February 20th is 3.1%. A $50,000 investment at a normal four-year CD rate of 3.1% would give you income of $1,550 per year, or $6,200 over the four-year period. The same $50,000 investment in the Target First Mortgage Program would give you $3,500 per year, or $14,000 over the four years. 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Buford Poster, you've got to love that. HD wants to go take a look at RIG. Rigatoni Trans Ocean Limited, RIG, is the ticker symbol. Wondering about support and resistance on these. The last three days, HD, we saw RIG hit resistance. That was the top of its daily profile. So 480 is a real key level for it to clear in order to continue to move higher out there, price below support from a monthly standpoint, meaning below the bottom of its profile. And on a weekly basis, the profile bullish and structure runs from 404 up to 515. So we would say a close above 480 should bring about the 515 level out there. So the question is, the question I have, did RIG form some type of bottom that you and I like to look at? Well, it just so happens that it did. If you take a look at the low out here, October 3rd, the bar following, bar number nine of a TD setup nine count, that made the low, there was your signal. And prices made it up to resistance. In essence, whenever you get a bottom or a topping signal, the very first thing to do is to look for support or resistance on the way up, on the way down, because that becomes your target. So the first target has been fulfilled inside of RIG based upon that daily bottoming signal out there. So you're wondering about support and resistance. So we'll leave it there. You also wanted to take a look at, I believe, BKCC. Let's go see what BKCC is. That is a BlackRock capital investment, BKCC. In this case here, below everything. Daily, weekly and monthly bottoms of their boxes. So there is no support from a TAS market profile standpoint. So let's pull over Stevie's other charts out here, see what we've got. We see no bottoming signal or pattern out here on the way to the downside. So let's get off of the daily and go over to the weekly. So we have on a weekly timeframe chart, intermediate term timeframe. This is going to be, it should be, a week or bar nine of a weekly TD setup nine count. The last nine count didn't do anything. It was a sideways move. When these counts occur, you'll either see a sideways move, a little bit of a hiccup, which is basically one or two bars to resume. It's moving that continued direction or an actual turn out here. So far it looks like bar seven is the low. That's at 475. The low today, 476. So today or tomorrow, we need to see price move below 475 in order for the count to offer you a potential bottom signal out here, but I'd be careful. That's what the weekly chart shows. So if the weekly chart shows a bottom signal, usually you'd see something on a daily timeframe. That was the reason why I said be careful out here. But the weekly says, yeah, it's trying to form a bottom. The monthly says it's an opportune time to form a bottom as price moves lower. That was with less relative energy. So well stretched to the downside out here. Wave count wise is in wave number six or letter F to the downside, but you need to see a bullish reversal signal before you'd even consider this confirming a rose momentum indicator bottom out here. So with regard to black rock capital, at this stage, we don't see a bottom pattern. Now the daily, maybe it could, let me see here, let me see if I pull this up here, under the covers real quickly. Pull this up. Yeah, so the daily, if the daily can make a lower low, get below the low of October 4th. You would see a rose momentum indicator signal get triggered. And so keep watching BKCC. Keep watching for price to push lower, push even lower, and then start to look for a bullish reversal candle because of the daily and the weekly chart, as well as the monthly that we looked at, no go as we speak right now, black rock capital investment, unless you know something that others don't. I just don't see it in the chart out there. So HD, thanks for writing in. Always good to hear from you. I hope that that helps you out. And of course, folks, I want to hear from you as well, although it's getting late in the show to get those emails and be able to go take a look at your requests. But let's go take a surf around, see what else it is that we can figure out inside these markets. What's going on inside the New York Stock Exchange, Advanced Declined Oscillator is at about 60. 60 and change out there may be gunning for plus 150 where you could see then the next top inside the New York Stock Exchange. I don't have any topping signals. We've got a higher high in the Advanced Declined Oscillator reading and a higher high in price. So there's no divergence pattern, which is typically present when the New York Stock Exchange makes its market top out there. We don't have that pattern in play. If I take a look at the New York Stock Exchange itself, let me switch over to the daily indexes out here. And the New York Stock Exchange is in bar number five, wave number four, wave number four. Baz likes to say at wave number four something else can happen. The last time we saw wave number four on the way up, the something else was just a sideways move. And so I can't tell you whether that's going to occur this time or not. But I don't see any topping signal as we speak. Speak of right now inside the New York Stock Exchange out here. I would more so be focused on the Advanced Declined Oscillator reading and price and what it's doing and looking for those divergent patterns or the plus 150 level to be looking for some type of potential top. Gold. Well, we can go look at gold. You know what? Now I'm just trying to see what else is it that I can look at here? I'm just kind of scanning my screens. Scanning my screens to see if there's something that's really pertinent, helpful to you in identifying what the market is. So let's just take a look at the XLK. I don't know if there's anything really helpful here or not at this stage. It did pull back today. It potentially could be in wave number seven. That was from a couple days ago. I don't really like to... It is for the way that I do the counting valid but because there was wave number five to the downside it's more likely on the wave three to the upside inside the XLK. Maybe today price was testing support or close to support at $81.16. It didn't get totally down there but nothing broken down in the number one dog inside of the S&P 500, the XLV sector. Is it doing today as a close above resistance? Resistance being $91.91 where it last broke down. The last level of resistance here is $92.52. Now this made a nice roads momentum indicator bottom out here. If price can clear $92.52 doesn't have to be today. If it can close above $92.52 this thing is headed higher. Today is going to be day number five of a TD setup nine count. Modders will look at the XLF out here so you've got the top three sectors making up a substantial percentage portion of the S&P 500. In this case when price pulled back inside the XLF it was right back to its breakout support at $26.41 that was back here in October. October the third probably October third. Yes that's what it was. Nothing bearish about in fact if anything the XLF is bullish because the green line turned red and then back to green on October 14th and price was testing the oscillator and change line out there. So all that the XLF needs to do is clear $28.29 that's the top of its current daily profile to continue to motor on the higher price. Maybe what it does is it sets up a oh that's interesting. Maybe what it does is it sets up a TD setup nine count top. So right now we've got the DAWA 43 S&P 11 and the NASDAQ 125. Since 1984 Basil Chapman has been using the Chapman Wave methodology to advise traders of his expert market opinion. 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If you're a trader in the market looking for exposure to gold or gold mining equities then now is a perfect time to sign up for Tom O'Brien's Gold Report. The summer is over, gold is trading back above $1,500 and the 10 year treasury is hovering at around 1.5%. Tom O'Brien has been writing his weekly gold report for almost 18 years. There's no one that knows more about how the gold market trades and how gold mining equities react. New subscribers get a 30 day money back guarantee so you have nothing to lose. Every Monday morning Tom publishes his weekly gold report with coverage of gold, silver, bonds, the XAU, HUI, GDX, the dollar as well as more than 30 different mining equities. As of September 3rd, gold report subscribers have five active open positions with an average unrealized profit of almost 38% for each position. To see for yourself the types of profitable trades that are recommended within the gold report sign up today by visiting TFNN.com. You know what's cool? Taking something that's good for you. Something specifically formulated to help with weight loss, better sleep, stress reduction and the need to detox. Nicar, hunter and gatherer ancestors found all their nutritional requirements for health in their wild environment. But today our food sources no longer contain the vitamins, minerals and nutrients our bodies need to stay healthy and strong. That's why we need primal edge daily nutrition. It includes a special blend of ionic, soil based vitamins, minerals, fatty and amino acids in an easy to use liquid form. Primal edge is powered by highly concentrated folic and humic acids, nature's preferred delivery system. They have been called miracle molecules because like sunlight, air and water, life cannot exist without them. That's right Paige, they ensure we receive all the nutrition we need to be healthy and thrive. We take it every morning. This is David White.  Folks, there he is, Buford Pusser. Buford Pusser from walking tall. Real guy, right? Real, you know, he was a one man wrecking crew in Tennessee back in the 70s out there fighting corruption and all that kind of stuff out there. Moonshining I believe it was, just you know the whole nine yards so to speak. Okay, so what are we gonna do here? You know look, here's the deal. Here is the deal, the tug of war, the fight between bulls and bears, definitely on. Now we say definitely on because as we took a look at earlier when you take a look at those short term timeframe signals here, one hour, two hour, five hour. They're all showing topping patterns or signals that are out there. So for example, let's just go look at the, we got signals in the five hour just to kind of take a, as we close the show what does that mean out here? If we look at the five hour timeframe chart for the EES many years we know price is moving higher doing it with less relative energy out there. At this stage here we don't have a bearish reversal signal or close below Stevie's green line which is 29.97. Bar number six is unfolding that we'll complete at 2 p.m. I believe. So you know, price is getting stretched out here but the stretching can go away with some type of strong momentum to the upside. So it's just a potential pattern out there when you look at the EES many. If you look at the two hour timeframe chart here in the EES many it's got the confirmed signal. It's got the, we've seen several confirmed signals out here but price hasn't been able to bust through support and real support out here on a two hour timeframe between 29.66 out there. So again, it's just a tug of war between bulls and bears out there. That then says, okay, what are the daily messages out here? You know, no matter how we skin this cat, not that we want to skin a cat. The message right now from the EES many, it's bullish. The NQ, it's bullish. The Russell's actually bullish but maybe resistance at 1548 and the Dow is the only one in check right now. 27.042, that's the key number to be watching because if you see it close above that you've got bullish messages across the board on the daily timeframe which will roll over the short term timeframes eventually. So folks, stay tuned. Thanks so much for being here. Two more great hours up. Polar bear from three to four, two to three and Obi-Wan Kenobi from three to four. I'll be back with you tomorrow. Thank you.


Is a marine engineering major or a marine engineering degree worth it? That's what we're going to be talking about today and we are going to jump right into it. What exactly is marine engineering? Marine engineering is all about researching, designing, constructing, and developing anything that floats in the ocean, so any type of marine vessel. This is going to include ships and submarines and any sort of parts that go inside of them. This is going to be very similar to maritime engineering or naval architecture. There's going to be a lot of engineering of course but you're going to have mathematics, science, and a good amount of drafting as well. Now at this degree you could become a marine engineer of course and naval architect. You could also work on all kinds of different shore side supervisory or managerial positions. In a lot of these careers you would of course be testing the naval equipment making sure the components are working and that they're not going to cause the ship to sink in the middle of the ocean. There's going to be a lot of budgeting preparing contracts, scheduling ships coming in and going out of different ports. There's a lot of routine maintenance that has to be done with ships and it has to be done in a timely manner so you're going to be working with a lot of contractors and making sure everything is scheduled properly. Now whenever I talk about these degrees I like to go over four different sections and the first one we're going to be talking about is going to be earning potential or salary. Now when you graduate with this degree according to pay scale you're going to make around $74,000 a year starting out and $125,000 in mid-career pay. You can compare this to a really high paying degree and a very low paying one and you'll see that it is on the higher side. If you become a marine engineer or a naval architect you'll expect to make around $92,000 a year. If you look at how much they make over a lifetime you'll see the engineering degrees in general make about 3.5 million which is the most out of all different majors. Now this is according to the latest census and so this data is now and then maybe 40 years back or so so this might not necessarily be true 40 years into the future. But overall without a doubt this is a very high paying degree. I'm going to give this one a 9 out of 10 when it comes to salary. Next on the list we're going to be talking about satisfaction and I divide this one into job satisfaction as well as meaning. Now meaning is how much you think your career positively impacts the world and according to pay scale this one has a 64% and again you can compare this to one that has a very high meaning score and one that has a low meaning score and you'll see that it is on the higher side. Now when you look at meaning score with a specific career of marine engineer you'll see that it's around 53% which again is above average slightly and then when you look at job satisfaction you'll see that it's 75% which is definitely above average and again you compare it to one that's really good and one that's bad. So if you're someone who really loves ships, sailing, being out on the ocean, all that sort of thing this can be a really good one for you. You're probably going to enjoy your job and it's going to have a lot of meaning for you as well. Now when it comes to job satisfaction versus meaning and which one's more important that's going to be different from person to person. In my experience job satisfaction is better on a short-term basis but meaning might be more important in the long run. Now when it comes to how much people regret their college majors engineering is the third least regretted type of college major only around 15% of people regret it and the main reason is because usually if you want to get some of those really high up their jobs right off the bat you're going to have to get an advanced degree so probably a master's. Now I always like to mention here that sometimes it has more to do with the industry you're in the company you work for the people you work with your location etc in terms of how much you enjoy doing your job as well as meaning sometimes even and so keep that in mind this is extremely subjective for one person it could be one out of ten for another person it could be ten out of ten. I'll say this one is kind of similar to aerospace engineering in that if you're someone who really loves airplanes you know aerospace engineering might be great for you if you're someone who really loves boats being out on the ocean submarines if that's you know something that you're really passionate about this could be a great direction for you to go. So with that being said I'm going to go ahead and give this one an 8.5 out of 10 when it comes to satisfaction. Next on the list we're going to be talking about demand maybe the most important one because at the end of the day when it comes to careers it's all about supply and demand. Now with this one if you want to become a marine engineer or a naval architect unfortunately I have some bad news for you right now there's only around 11,800 jobs available and it's growing at 1% over the next 10 years so that means only another 200 jobs are going to pop up or be created over the next 10 years which is not great but with that being said there's not that many people graduating with this degree it's a relatively rare major so that is a plus side and on top of that there are a lot of other different career paths you could end up going down some of them loosely have something to do with marine engineering like you might be working on a shore you know managing things making sure the correct repairs are done to the ship correct upkeep for instance and then some career paths you can go down that pretty much don't have anything to do with marine engineering but just the fact that your engineering degree is so well respected will get you into the door. Now of course 2020 is throwing the stats off quite a bit but with that being said 2018 for instance STEM degrees were some of the least likely ones to have people who are unemployed but with that being said STEM degrees are known for being pretty good when it comes to unemployment most people who get STEM degrees end up getting a job and engineering degrees are going to be one of the better STEM degrees overall so you likely as long as you do your due diligence will not find yourself jobless. Now with that being said when you look up the term marine engineering degree on monster.com only around 816 job postings pop up that have that as a keyword in their description. You can compare that to one with a ton of demand like computer science or one that doesn't have much demand at all like anthropology and you'll see that it's definitely on the lower side there's not a lot of employers out there that are looking for people who have marine engineering degrees this is a pretty specific degree and what I mean by that is it'll teach you skills that are extremely specific and that might pigeonhole you just a little bit but the good thing is that engineering degrees tend to be relatively well respected overall and so even if you don't end up working as a naval architect or a marine engineer people will likely hire you for jobs that might even be totally unrelated when you look at the degrees that are in demand by the biggest companies out there engineering almost always comes in as number one or number two even when companies aren't specifically looking for people who graduate with this major when they see that you have a marine engineering degree they're probably going to think that you're very smart and very hardworking and so they'll give you a chance but overall I have to be honest with you guys when it comes to demand it's not going to be one of the better engineering degrees out there it does kind of pigeonhole you a little bit so I'm going to give this one a seven out of ten next we're going to be talking about x factors and this is anything that I didn't mention before that I think is still important so first thing I want to talk about is I'm going to go back to the whole how much money you make over a lifetime thing and like I said before engineering degrees will make around 3.5 million over a lifetime but it gets even deeper than that you can make good money as an engineer pretty much no matter what career path you end up going down so if you look a little further down the list for instance if you end up going into arts and media you still make around three million dollars over a lifetime even though most people make less than average and you see this for pretty much every career you end up going into engineers tend to do very well or could be the practical problem solving skills that you learn as an engineer tend to transfer over to just about anything you end up doing now when it comes to skills zip recruiter doesn't have a specific skill of marine engineering the closest one would be mechanical engineering and that has a 77 out of 100 and again you can look at a really good one and a really bad one and you'll see that it's definitely on the good side of things additionally this is one of those degrees that is not very likely to be automated so according to willrobotstakemyjob.com there's only around a 1% chance that a marine engineer or naval architect job is going to be automated same thing goes without sourcing in my opinion a lot of the time with engineering type jobs you do need to be there in person you need to be able to touch things talk to people who are there you have that technical expertise but you also have a deeper understanding so you're almost like the person who is the middleman between a scientist and a tech person right so the technician that goes in and fixes stuff and a scientist engineers almost have both of those people's skills and then you add a little bit of practical creativity in there because a lot of the time engineers will imagine something in their head and then they have the skills to make that become a reality you know right in front of you now another thing I'll mention about engineering is it is one of the degrees that create the most millionaires and I believe the reason for that besides the fact that it pays really well is because of the fact that it teaches you practical problem solving and it leads a lot of people to become entrepreneurs later on in life there's pretty much no ceiling on how much you can make as an entrepreneur you can scale your business as high as you want to and so they're more likely to become millionaires of course I think that's the main reason but you know the high salary doesn't hurt either but with that being said I always like to make sure to tell you guys that engineering is very very tough okay I was in a scholarship hall with around 50 guys I think maybe five to ten of them were engineers and you know another 10 of them were business majors the business majors had a lot of fun okay they were partying all the time they're having lots of fun the engineers did not have so much fun I'm just telling you that right now and then I was somewhere in the middle with my science classes engineering always ranks as one of the most difficult majors it has one of the highest dropout rates and not just because people decide that they don't like to do it like a lot of the other majors there's a high dropout rate because people literally can't do the classes like they they drop out of the classes because they're getting f's so with that being said when it comes to x factors I am going to give this one an 8.5 out of 10 so some of the pros here the salary projection is great I mean you're going to make quite a bit of money if you're able to get a job this is an ocean related career so if you're someone who likes being around the ocean and you know likes being on ships maybe you're passionate about sailing something along those lines it could be great for you there are a lot of offshore and shoreside jobs for people who graduate with this one a lot of those offshore jobs tend to be really well paying so for instance if you work on an oil rig some of the cons here are that it's a very rare degree okay very rare I think less than a thousand people graduate with this one every year and so not that many schools are going to offer it some of the best jobs are going to require more studying and experience maybe a master's degree for instance and there aren't that many job openings employers are not out there actively looking for someone who graduated within a marine engineering degree however if they see that you got this degree it's going to be well respected so you're probably going to be able to get hired so overall here the score is going to be 8.25 out of 10 this is a good one for the right person now if you are the random miscellaneous things I didn't mention here a lot of the time if you are a marine engineer that's on the ship itself it's going to be kind of like one of those sci-fi movies where you're the engineer on the ship where basically the engineer for whatever reason is a mechanic like you're going to be actually working on the ship while you're on it there's a lot of engineering jobs out there that are kind of desk jobs you're not necessarily touching things but you'll likely be very active as a marine engineer if you're working on a ship or maybe on a submarine so it's a lot more hands-on than a lot of other types of engineering degrees and on top of that if you are working on a ship that means you're going to be away from families you'll probably be working during the holidays etc now with that being said there's a lot of onshore jobs as well where you'd be working at some kind of dock behind a desk and you could argue that many of these jobs could be done by someone who graduated with a mechanical engineering degree so that's kind of a downside a little bit of a red flag depending on what career going for there's probably also going to be some pretty extensive licensing and certification requirements but yeah if you'd like more help doing research and you don't want to wait around for me to put out a video go ahead and check out my college degree ranker down in the description below it is in my opinion the best college degree resource that you will have when you're doing you know research on which degree that you want to go for if you haven't done it already go ahead and gently tap the like button in order to defeat the evil youtube algorithm hit that subscribe button ring the notification bell comment down below any thoughts comments criticisms sharing the video helps a lot if you have anybody that's interested in this one and before you leave check out my other videos right here i made them just for you


In this lecture, we will discuss properties of context free languages, and first we observe certain trivial properties, and then we will ascertain some properties connecting to context free languages, which you know you will look at in parallel to what are called properties concerning regular languages. So, this properties of context free languages, so point one it is very clear from the definitions of context free grammars, you can quickly understand that the class of context free languages is closed with respect to union, this proof is very simple. If you take two context free languages, let L 1 and L 2 be 2 CFL, so that means you have say G 1 is equal to N 1 say T 1 P 1 S 1 a CFG such that the language generated by G 1 is L 1, and similarly you can have G 2 say let me call L i for i is equal to 1 or 2, I have two context free grammars.  Now, this language it is certainly over union of the terminal symbols, and now production rules P I let you know in S. So, in this case the production rules you take P 1 union P 2, and you give new rule S goes to S 1 or S 2, if you set grammar like this you can quickly clearly see the productions in P 1 are in the form for context free grammar, and for P 2 also. Now, what are the two new rules I have introduced S goes to S 1 and S goes to S 2, these two are you know satisfying the conditions for the context free grammar, and thus you can see note that this G is a C F G, and now you can ascertain that the language G is a C F G, and the language generated by G is simply L 1 union L 2 that one can observe. Because if you take any string generated by this grammar you have to start from the start symbol S, and you have to take one of the branches S 1 or S 2, if it is going to S 1 then you can generate the strings of L 1, if it is going to S 2 you can generate the strings of L 2. So, that you know any string which is generated by this in L 1 union L 2, and conversely what are the string which is in L 1 union L 2 you know either it will be L 1 or it will be in L 2. So, you know if it is in L 1 you can generate through that through S 1 thus you can generate that through S also, so that it will be in L of G similarly. So, you can observe you can prove that this construction works to show that context free grammars, so context free languages are closed with respect to union. Now, if you look at intersection that will be a question to us, the question is the set the class of CFL's closed with respect to intersections, and you can question that this is closed with respect to complementation etcetera the set theoretic properties related. We will address these points little and now if you ask about these are set theoretic thing, now if you look at the concatenation again. So, the result is the set of or the class whatever the set of CFL's is closed with respect to concatenation how as earlier you know you let L 1 L 2 be 2 CFL's consider the respective context free grammars say G 1 G 2, and now when I am setting G here I consider the production rules you know of this form, because this is P 1 union P 2 union this S goes to S 1 S 2 I will consider. So, here you require the non terminals of the first one of the second one union a new symbol S, and for concatenation anyway this T 1 union T 2 and P S. If you have this again this new production rule I have a single rule here, this satisfies the criteria for context free grammar, so that you know you can note that G is a CFG, and you can observe that language generated by G is L 1 L 2 how come? If you start from S you have to use this if I take any word which is in L of G I have to start from S and produce that word W, if W is in L of G I require this, but you look at the first step from S I have only one rule. So, that means I should use this S 1 S 2 and after that infinitely many steps I might be producing this W. Now, corresponding to the non terminal whatever that we are generating the terminal string the portion of W that you can generate in L 1. Similarly, corresponding to S 2 whatever that we are generating the portion in this W that is in L 2, so that this W can be written as x y for x in L 1 y in L 2, so that it is in L 1 L 2. And similarly you can see the converse that means if you take any string in L 1 L 2 you will have two strings say x 1 x 2 x is in L 1 x 1 is in L 1 x 2 is in L 2. Now, since x 1 is in L 1 you can generate that in the grammar G 1 x 2 is in L 2 you can generate that in the grammar G 2 and thus you have the respective production rules to generate this x 1 and x 2. Now, if you take the if you start the derivation what are the derivation that you have got from S 1 to x 1 you have got a derivation in G 1. And similarly for x 2 you have got a if you start with a string W is in L 1 L 2 this W is of the form x 1 x 2 and for x 1 is in L of G 1 and x 2 is in L of G 2. So, I have these derivations and now you just have to start use this production rule S 1 S 2 and then use this derivation and produce from S 1 because the derivation G 1 will be derivation G also because all the production rules of G 1 at P 1 the production rules are already there in G. So, I can make that as a derivation in G also. So, I have x 1 this and after again finitely many steps x 2 can be made this x 1 x 2 thus you see that you have a derivation this in G. So, this is a derivation in G. So, that this x 1 x 2 that is what is W is in L of G. So, we can observe these things. So, this is one side to observe that L of G is continue in L 1 L 2 this is a other side to observe L 1 L 2 is continue L of G. So, that this grammar what we have constructed here that generates L 1 L 2. So, that you know the class of contextual languages is close with respect to concatenation. So, regarding this set theoretic questions whether the class of CFLs is close with respect to intersection, complementation before going to such questions and many other properties. Let me just give you the pumping lemma for CFLs which you know it is something parallel to the one you have worked for regular languages. So, let me first state the lemma because I do not have to give much introduction for this because you have already worked for such pumping lemma for regular languages. The philosophy is similar what pumping lemma says for any infinite context free language L of course, this we will be observing that it is true for finite language also. But, anyway I will work for infinite language here. So, for any context free language L there exist a constant n such that for all w in L with length of w is greater than or equal to n this w can be written as u v x y z such that the length of this v y the second component and the fourth one length of v y is greater than or equal to 1 and length of v x y the middle one this v x y these three components that is less than or equal to n. And if you pump the strings v and y simultaneously for i number of times that means for all i greater than or equal to 0 u v power i x y power i z is in L all these strings will be in L. So, now look at in case of regular languages every string you will be splitting into three parts you will be able to split into three parts such that the middle string is non empty string and if you pump that string for any number of times the resultant strings will be within the language that is what we have observed in case of a pumbig lemma for regular languages. Here what is happening a string can be split into five parts and among this five parts say u v x y z when we have split it this v and y at least one of them is non empty when I am say this carnality of v y is greater than or equal to 1 that means at least one of them has to be a non empty string and the middle portion that v x y these three strings together you can always produce such a way that this length is less than or equal to n what are the number n is existing. And now if you pump v and y simultaneously for any number of times the resultant strings will be in L. So, the philosophy is similar and the applications are also similar. Now, I will give you an idea that how we will produce this result. So, the idea is as follows now you look at if L is a context free language you have a grammar corresponding to that say some n t p s and if you now we have to identify the number n we have I have to come up with a number n I will tell you what should be that number. And now what how the how this number should be if you take any string w in L of g whose length is greater than or equal to n I should be able to write this w in five parts u v x y z. So, this v y at least one of them is non empty. So, that is what is the break up we require and if you pump these two portions any number of time simultaneously the resultant string should be in the language. Now, w is in L of g you have a derivation for w you have a derivation for w what I will what I will show here is I can always have this derivation of the form because I will find a number n such that this derivation can be for this w the derivation I will I will get things like this say u some non terminal a z I can always produce things like this or you know this u and z you may be producing later also does not matter. So, I will have a non terminal symbol this non terminal symbol will occur after you know after production of some strings that is you know u v a y z and then this a I will be able to terminate x y z. So, if I can show that I will have a derivation with the given context of this form then I am through this is what is w why because once I have a situation like this you see what is happening this non terminal a is producing the string v a y. Now, this a once again we can produce v what is called v a y after finitely many steps once again. So, that you will have double y and if you once again if you use you are getting triple v a triple y and also you see that a is producing x infinitely many steps. So, I have this also a produces x infinitely many steps. So, this is also there in the part of the derivation thus after finitely many times if you use you will get you know v power i a y power i you can get like this. And then if I use this I will get v power i x y power i because a is a can be termed with the terminal string x. So, I will get always like this thus you see I have a derivation in this grammar of this sort. Now, you look at what is happening here in this derivation if you observe if I can have such a derivation what is here the a non terminal symbol which has occurred once is appearing once again in the derivation of a string whose length is bigger than or equal to that n. So, that is what is essentially the fundamental idea once it reoccurs once a non terminal symbol reoccurs I would be able to produce derivations for v power i x y power i within the portion of that. And then you know I can produce the strings in the required as mentioned in the statement. If this is clear we can get the idea how we have to proceed. So, what we will do I will connecting to this suppose if I draw the derivation tree for this this is a start symbol let us assume this way. And what I have here I am getting say for example, a here once and once again if I am getting a here within the purview of this a whatever is because you see contractual grammar. So, every non terminal symbol will have production rules there is nothing to do with other symbols adjacent to that for a if it is producing x and this a if it is this tree if it is producing the portion v y this is the leaves of this derivation tree. And now what are the remaining portion here that is u z this portion. Now, the derivation tree if I can have this a reoccurring now connecting this sub trees will be having this way and thus whatever the way that I have described here you know this such a derivation a has occurred once again and thus I will be able to produce the strings of the form u v power i x y power i z in the language a language generated by g. So, now you look at whenever you know if I am looking forward for repetition of a non terminal symbol. Now, you put a cap on it that means you consider a number you consider a number such a way that if you take any string whose length is bigger than that number in its derivation tree you know you require this non terminal symbol to be repeated there should be repetition of non terminal symbol this is the fundamental idea that I have just discussed accordingly you know. So, what essentially we have to set the number in any string if you look at the derivation tree in a branch I should have a non terminal symbol repeated there taking this into count if you have if you if you consider that number then what are the string in the language whose length is bigger than that particular number you take the derivation tree of this form. Then you can manage to show that you know it is littered into u v x y z and of course, we have to observe that we have to have this splitting such a way that at least this v or y should be non empty and of course, the extra criteria we had put the length of this should be less than equal to that number all these things we require these are all extra conditions. But as a bare minimum you can understand that it will be split into 5 parts in which this v and y portions are at least non empty and u v power i x y power i z for all i this will be inside L that is what we have to observe. So, what do I do in this connection to get this extra properties what instead of considering an arbitrary contested grammar I will consider a contested grammar which is in c and f you know Chomsky normal form. So, in Chomsky normal form every production rule is of the form you see that a goes to b c a goes to a of course, if connecting grammar if it is in Chomsky normal form in the language if you have empty string except empty string everything else you can generate you know that. So, these are the types of production rules that you have and now if a grammar is in Chomsky normal form you know this you can quickly understand this property. So, let me write this lemma it is not difficult for you to understand let g is equal to n t p s b a c f g which is in c and f Chomsky normal form. So, generating a language in c and f if a parse tree of a word parse tree of a word w generated by g is of height h then you can observe that the length of this is less than equal to 2 power h minus 1 you see what happens I just of course, this you can prove by induction I will just demonstrate I illustrate this two example for example, I have like this. So, since it is c and f I can have say like this if the situation is once again I have non terminals I will have like this then say for example, a 1 a 2 and if in the case you know say a 3 or b whatever now you look at because it is in c and f you know the length of what happens now if I consider the complete binary tree here. So, the possibilities I can in fact, extend if I am looking for the height here 3 say b 1 b 2 say b 1 b 2.  So, to this level if you come now you understand now at any level suppose if you are not you are terminating at this level itself now the lesser number the, but the maximum you look at that if it is of height you know here 3 you see that 2 square here. So, if the if it is of height 3 you know 2 power h minus 1 that is the maximum length string that you can produce if it is of height h any parse tree of height h can produce a string of length of length maximum 2 power h minus 1 maximum this is the length. Now, in fact you can observe this result by induction by induction on this binary trees you can observe this result I will use this result. Now, so let me consider this Chomsky normal form in the in the present context. So, for proof of this result let G equal to N T P S be a contractory grammar in Chomsky normal form generating l minus singleton epsilon right. The Norton mills set suppose the size is k and set the number n 2 b 2 power k now you will understand because just know the result what we have discussed is if it is of height h the length of you know the string will be maximum 2 power h minus 1. So, I will consider this n equal to 2 power k now you consider the string w in l of length greater than or equal to n take any string whose length is greater than or equal to n now since it is the length of this is greater than 2 power k minus 1 any parse tree T of w in G must have a path of length at least k plus 1 because the length of this thing is greater than 2 power k minus 1. So, you should have at least one path of length at least k plus 1 now let me draw a picture in that sense. So, you consider a parse tree of this w. So, you should have you should have you should have a path of length at least k plus 1 because whose length is bigger than or equal to n since it is greater than 2 power k minus 1 I should have a path of length at least at least k plus 1. Now, the last node is anyway terminal node some terminal node will be there and then here before that a non terminal node will be there. So, these are all non terminal nodes on this of length at least k plus 1 at least k plus 1 length now you look at. So, let me say that path will be p. So, how many vertices will be there if it is of length k plus 1 there are k plus 2 vertices will be there on this path or at least k plus 2 vertices. Now, you know the last node is a terminal node and at least then k plus 1 non terminal nodes will be there on this path. On this path p at least k plus 1 non terminal. So, whose labels are non terminal symbols. So, at least k plus 1 nodes whose labels are non terminal symbols. So, you will have like this and thus you see if there are at least you know k plus 1 nodes who labeled are non terminal symbols, but how many non terminal symbols we have there are only k non terminal symbols.   So, whatever that it is getting repeated for example, this node label and this node label assume they are same. For example, say you know the label is a if I am writing and the node say it is close to this terminal node that means let me call v t and the node which is close to the root I may call v r whose labels are same the label is the label of v r and v t assume it is a labels are same.  So, let me assume the first node which is getting repeated say v t label and v r label I am just writing because v r which is close to root and v t which is close to this whose labels are a. So, from the leaf node on p go above and check the first k plus 2 vertices we will find 2 vertices v t v r whose labels are same non-terminal symbol say a this is how we have taken a label. Now, note that the portion of p from v r to leaf node is of length at most k plus 1. So, the subtree t r with root v r that represents the derivation of subword say w dash of w of height at most k plus 1 from here whatever is this this w is the entire word of course, this subtree let me call it as w dash. Now, you look at how many nodes I have visited k plus 2 at the maximum k plus 2 nodes I have visited and therefore, the length of this path is you know the length of this path is k plus 1. Now, you see the height of this tree is maximum k plus 1 why is because the height of this is maximum because p what we have considered that is the longest path in the entire tree in the entire tree I have considered a longest path. Therefore, you know here this portion should be longer than any other path within this subtree also if I have something else then it cannot be longer. And therefore, the height of this thing is at most k plus 1 thus what do you have the length of this word is less than equal to 2 power k length of the word because whose height is maximum k plus 1 and from the result what I have just discussed the length of the yield this from this lemma you can observe that it is less than equal to 2 power height minus 1 and therefore, the length of this w dash should be less than equal to n. Now, you see if you consider the subtree now if you consider the subtree rooted at this v t if this is a subtree rooted in v t which represents the derivation of sub word x then w dash can be written as v x y because this w dash is connect is the yield of this subtree rooted at v r if you consider the subtree rooted at v t the yield of this subtree if I call it as x then this w dash can be written as v x y this entire portion w dash. So, this portion is x now you understand this point because I have considered c n f this is node a and this a goes to say for example, b c because it is in c n f I will have you know this subtree here which is marked rooted at this v t this should be a subtree of you know a subtree of a tree which is rooted at b because I am having you know two branches here from this node. So, this subtree will be entirely within the subtree rooted at b or it should be within the subtree rooted at c because you look at that say a now the rule say for example, b c is like this now you have a tree connecting to this b and you will have a tree there will not be anything common. Now, what are the subtree I am showing rooted as v t this v t will be therefore, within this or within this it cannot be you know this v t cannot be in the common of these two and therefore, from this you can observe that other than this portion x you know when I have c here suppose if it is within b the c should get terminated and at least you know some string some yield you will have. So, when I am writing w dash is equal to say v x y. So, the remaining portion other than x should be at least you know you should have at least one symbol and thus it has to be non empty the length. So, this is the argument I am placing here since the first production used in the derivation of w dash at v r must be of the form a goes to b c for some non terminal symbols b and c the subtree this t t must be completely within either subtree generated by b or the subtree generated by c and therefore, you see at least one of this b or y should be non empty. So, the string v y length should be greater than equal to 1 thus what do I have this a infinitely many steps I am producing v a y and this a infinitely many steps we are producing x where v a y length that is what is w dash is less than equal to n that is what we have observed and also with this argument we have observed that v y length should be greater than equal to 1. And hence because of these two derivations we have for all i greater than equal to 0 we have a produces infinitely many steps v power i x y power i. So, this is what essentially I have mentioned that we will give a derivation within the given derivation as a sub derivation that a non terminal symbol will be repeated and it produces strings of this form v power i x y power i once I have this then I am through. So, I can conclude this result now note that the string w can be written as u v x y z for some u and z because this is the rest of the portions other than the subtree what we have discussed. So, the derivation will be of this form this s produces u a z etcetera and now the derivation connecting to this if you place it here you can see that all the strings u v power i x y power i z for all i will be in the language l. Thus you see every string w of length greater than equal to n what are the constant that we have set here the constant is in this particular context I have set n equal to 2 power k because we have considered Chomsky normal form and you can observe this all the strings u v power i x y power z will be in the language l. So, this is what is pumping lemma for context languages and you can compare with pumping lemma for regular languages and understand this better. Because the philosophy is similar the way that we are working there we have worked with the states if the proof is through you know finite automata here we are working through the non-terminal symbols here. But what is the philosophy once again if you look at you know I have to produce the derivation of this form I have to produce the derivation of this form as I had explained here. Once I had produce the derivation like this I can always produce the strings u v power i x y power i z in l for all i. So, for that purpose we have considered you know the tree in which we have considered longest path and such a way that you know the non-terminal symbol is repeated. So, the constant we have to set accordingly. So, we had set accordingly and we have produced this result. Now, let me talk about applications of this pumping lemma because you see in case of regular languages the pumping lemma you have used to observe certain languages are not regular. Similarly, here in case of context language also we use this pumping lemma to observe certain languages are not context free. Let me just give this example if you consider the language l a power n b power n c power n m greater than equal to 0 this is not a context free language. How do I observe this? Suppose l is a context free language. Now, as per this pumping lemma you should have a constant let me say n naught be a constant as per pumping lemma for CFL. Now, as we have worked for regular languages here also same debate if you choose any string w whose length is greater than equal to n naught what pumping lemma says if it is if it is a context free language we should be able to split it into 5 parts in which you know at least one of them is non-empty that we are y such that if you pump those strings simultaneously for all the powers the resultant string should be in the language. Now, I will give you a string which fails that particular condition and so that we say that our assumption is wrong. So, when I am assuming it is a context free language I get a constant n naught as per the pumping lemma. Now, let me smartly choose the string say because here the strings are of the form a power n b power n c power n I am particularly choosing you know this a power n naught b power n naught c power n naught you see the length of this string is 3 n naught and therefore, this is greater than or equal to the length n naught number n naught length of this thing. So, if it is split it into any strings of the form u v x y z into 5 portions if this w is split it like this with the which satisfies the conditions that v x y length is less than equal to n naught and at least v r y is non-empty once I have once I take this restriction v x y length is less than equal to n naught you see how this portion v x y looks like how does it look this v x y since it is of length less than equal to n naught it will be within a s or within b s or within c s or you know you can have some a s and some b s of course, you cannot have a s b s c s because the length is length maximum n naught. So, this can have if it is in the border you can have some a s and some b s or you can have some b s and c s, but you cannot have all a s b s is together. So, now you see what do I do as in case of regular languages I have chosen this string now as shown below this u v power i x y power i z is not in l for some i for some i I will produce that which contradicts pumping lemma. So, that the language is not a context free language that is what is will be the conclusion if I show that for some i u v power i x y power i z is not in l. So, we have the following 5 cases as I had just mentioned for v x y for some m m 1 and m 2 it either it can be of the form a power m this v x y or it is of the form b power m or it is of the form c power m or if it is common to the portion this a s and b s I will have a power m 1 b power m 2 form or it is of the form if it is common to b s and c s b power m 1 c power m 2. If I argue for a s then it will be similar for to these 2 cases if I argue for one of this the other thing will be similar. So, we discuss the cases 1 and 4 other cases will follow in a similar manner let me consider the case v x y is of the form a power m then w that is u v x y z it is of the form a power k 1 because when a power m when I am saying this side and that side you can have some a s. So, this k 1 k 2 you know greater than equal to 0 because if a power m is equal to a power m naught then you can have you cannot have any number of a s either side but anyway this is the generic format when v x y is of the form a power m. So, this u v x y z if it is in this form since this v r y is non empty since v r y is non empty that means within this a s you know at least 1 a if you consider when I am pumping this v s and y s whatever is non empty what will happen the number of a s will increase but the portions in this z you know you have v s and c s which remains same because I am just pumping the words v and y the number of a s here for example, here within this v y if 1 a if it is there somewhere it has to because the length of v y is greater than equal to 1 if I keep pumping the number of a s will increase number of number of a s will increase and therefore, the number of a s will be different from the from that of number of b s and c s and hence what will happen you know the resultant string will not be in l. Similarly, if v x y is of the form a power m 1 b power m 2 if it is like this you know I have some a s here a power m 1 b power m 2 and the rest of the b s I may call it as b power k 2 c power n naught it is of the it is now since again v n y s when I am pumping I do not know v may have some a s y may have some b s you might be pumping them or you know v n y s may have only a s in which case when I am pumping them if it is i greater than 1 if I have if I raise the powers what will happen the number of a s or b s will increase whereas, the c s which are in the portion z you know that will not increase and therefore, as the number of a s or b s will be different from number of c s in the string this cannot be in l this cannot be in l. So, I can produce strings for certain powers which are not in l, but pumping lemma says that for all i it has to be. So, since I am producing the strings like this as observed now you have some i such that u v power i x y power i z is not in l which is contradicting pumping lemma and thus you can say that this language is not a context free language. Similarly, people can you know several other languages say for example, w w as a w belongs to a a b star you can observe that this is not context free using pumping lemma. Only thing is if you say this is context free language what you have to do you have to there will be a constant you have to now choose some string and observe that when you divide it any of the form u v x y z then by pumping v r y v and y simultaneously you will have certain strings which are going beyond the language. So, that is how we have to do now you can take this as an exercise and ascertain that this language is not context free some more languages I will display now that they are not context free you can observe them.


Hi, I'm John Collins. I'm an affiliate at the Berkman Klein Center, and I work on digital finance issues I also founded a little nonprofit in the state of Delaware called the first state fintech lab and among other things we work on Access to Opportunity so today I want to talk about the cashless economy I think probably many of you are wondering is there actually a cash economy and in the words of the Wu Tang clan cashrolls everything around me dollar dollar bills y'all and there are a lot of dollar dollar bills probably surprising to you in fact the cash economy in the United States is 2.3 trillion dollars Per year to put that in a little bit of perspective the overall gross Domestic product of the country the size of the economy per year is About 19 trillion dollars, so smart people here 2.3 out of 19. It's pretty significant Even though many of us probably don't use a ton of cash So think about like what you have in your wallet right now. I'll pull mine out I have a business credit card. I have a personal credit card. I have a debit card I do have cash because I won a bet this weekend at a Kentucky Derby party That's the only reason I have it and then aside from my wallet. I obviously have Phone right a smartphone in fact a cracked one, but it still works and so on here. I've got Venmo I've got Apple pay. I've got my Starbucks app So even in situations where I might not have my wallet I have this and I can access a lot of commerce nowadays via that and I'm not alone in fact the Federal Reserve has taken a look at How many payment mechanisms the average American has and 50% of us have six plus ways that we can pay for things? So you've seen you've seen that increase over time, right? There's only more fintech applications more types of credit cards coming out This is a really bad graph But I just want you to take a look at that dark line that goes down That's the amount of cash being used as the two other lines at the top there Which are debit cards and credit cards are increasing right and that makes a lot of sense right you're increased use of this Merchants are seeing this as well. So sweet green which is a luxury coleslaw merchant. They Found that about 10% of their customers use cash only 10. So they said you know what?  Well, it's not really good It's not good for everybody eight point four million people in this country are unbanked That's about six and a half percent of the population Where I spend a lot of time Washington DC About 25 percent of the African-American population is unbanked and about 36 percent are underbanked And so what happens is when you have populations that don't have access to financial services Then you create places where they must have access to financial services You exclude them and you create as these cities get more expensive more and more gentrified areas that that are exclusionary and the Civil Rights Act in the United States requires and in fact You know maintains that people have equal access to the enjoyment of public accommodations like retail goods so Cities and jurisdiction the governments are responding to this in different ways in fact, Massachusetts in 1978 Passed a law saying look you got to accept cash everywhere and you've seen more recently as these stores have Kind of put out these proposals other cities follow suit So the city of Philadelphia more recently the city of New York the city the state of New Jersey have passed legislation to say look You got to accept cash. We're banning these cashless stores And so where does that leave us unfortunately? I'm not going to be able to give you any solutions today But in this five-minute talk but on one side look We've got a system that that is making transactions easier and cheaper in some cases But it's excluding a large part of the population. So that's a problem Bands are our blunt policy instruments that certainly Solve the problem in part, but they they don't really get the underlying issue Which is we need to provide better access to financial services for people who don't have it Part of the solution might be innovation it might be sort of more fintech applications It might be regulation because a big part of the problem is that fees and Expenses related to financial services can be expensive, especially as a percentage of income But regardless what the policy focus needs to be on and should be on is making sure that more underserved Interrepresented populations more diverse groups of people have access to these services and to the wider economy. Thank you


Why narcissists disappear when you first met the narcissist They may have made you very happy They were very charming They were agreeable They were full of praise and compliments It seemed like everything was perfect They listened to you They seemed to recognize and value your abilities qualities and accomplishments They seemed to have regard for your feelings wishes and rights But then one day The narcissist disappeared They vanished from sight They left for a few days weeks or months and it may have been after a argument Or it may have been for no apparent reason They may give you an appropriate reason They may say that there was an emergency But as time goes by they begin to disappear more and more Because they're trying to punish you they may even threaten to leave you Or replace you with someone else When it wasn't long ago That they were telling you how much they love you And how they want to spend the rest of their lives with you But then suddenly they're no longer interested in you And they may never come back Because they've already drained you of everything You no longer have any use to them. You may be very sick and helpless You may be left suicidal or hospitalized And that is when the narcissist will abandon you forever They will only come back If they find out you've managed to recover If you're still able to give them what they want But some narcissist Will stay with you even when you're sick and helpless Because it gives them a sense of control And it makes it easier for them To put you through the endless cycle Of abuse and rescue But sometimes they're just waiting for you to die Or end up in hospital So that they can prey on you and exploit you Another reason why the narcissist might disappear Is because you've figured them out You've exposed them You know who they are They can't manipulate you anymore When the narcissist knows they can't get any more supply They're not going to waste their energy on you They will find someone Who is more susceptible to their manipulation But if that doesn't work out They may try to hoover you And that may even be a punishment To their new supply When they disappear They won't give you a reason They will give you an unjustifiable excuse Or they will start an argument with you So that they have a reason to leave Because they're busy with their new source of supply But when they do that You should realize that they were never really with you They were never really loyal or committed to you They were just waiting in the wings Until they found something new When the narcissist chooses to disappear You cannot control them You cannot change them You cannot stop them from doing what they choose to do Because it really has nothing to do with you Narcissists are going to do what they're going to do You just have to return to yourself And begin to question Why you're seeking love and devotion From the narcissist You may have abandonment anxiety Which is what they will use against you But you need to realize that you have the power in this situation You can choose when it ends By healing yourself By no longer fearing abandonment By no longer fearing being replaced by someone else Which is where I can guide you I invite you to book a coaching session with me At Narc Survivor the Cuddy UK Where we can talk about healing from narcissistic abuse Removing your fears and doubts about the narcissist And building a better life for yourself Thank you for watching I hope this video resonated with you Please like, comment, share and subscribe If you would like to donate My PayPal link is in the video description Coaching inquiries You can email me at coachinganarchsurvivor.uk Thank you for watching and I'll talk to you soon