Hey everybody, welcome to Friday. What is today? May 6th, 2022. Welcome everybody. This is gonna be a cool session. I'm gonna actually walk you through the five steps that I did to start running growing online business. Actually, several online businesses. So you want to stick around to the very end. I'll give you the exact process that I went through and exactly what you could do and how to be successful at this. It's not that hard once you get a certain concept that's gonna be number one in just a second. Before we get started, don't forget to what? Subscribe. Hit the subscribe button down there. Turn it from red to gray. Make use of this chat box guys. I'm over here watching it. I can respond to you in real time. Any questions you want to ask me, I'm there for you. Give me a thumbs up. Also, smash that thumbs up button. This is my little advertisement before we get going. I don't sell anything on this channel. You know, if you want to buy something from me, if you want to join one of my courses, you'll find that in the description below. So at any point you want to do that, that's fine. I never talk about that stuff. Also, don't forget to ring the bell. Don't forget to ring the bell because when you turn on all your bell notifications, guess what? Guess what? When you turn on all the bell notifications, you'll know when I upload a video or if I go live. So you want to do that. It's super, super important. So guys, there's only five things you need to do to be successful. And it's interesting because I remember when I first sold my first item online, it was $10. And I was, God, I was so excited about it. As a matter of fact, I was a single dad. I was still working my day job and my kids were in the family room and I came running in there and I said, I sold something online. And they were like, wow, that's really cool. I said, I know, right? Somebody give me money online. They said, how much did you sell? And I said $10. And they both looked at each other like I was insane. They both looked at each other like I was insane. They were like, okay, you know, but that wasn't it. The thing was I knew if I could sell $10, I could sell 20 or 100 or 1000 or a million. And I have sold millions of dollars online. And I want to walk you through that process today.  You are just indestructible. I think you're really going to enjoy this. And it's funny the other day I was talking to a friend of mine and he knew me when I was in my past job and I used to manage car dealerships. And he was in he was in the service department. He was a service guy. He's been a service writer and manager. And he works at a Ford dealership now and he's the number two guy at a body shop. And it's funny because he's worked I think four or five places in that 12 years since I left the dealership about four or five places. He's moved to different states and all kinds of stuff. And he's the number two guy at a body shop. Okay, so I just kind of get that in your brain. And I was talking about my business and he was talking about and he was saying, gosh, you know, you really got lucky. Which I hate when people say that because there's zero luck to this stuff. I mean, there's luck, but it's it's it's created luck. And I'll talk about that in a second too. But I said, Do you remember when I quit and everybody thought I was crazy, you know, quit because I had a decent paying job. It wasn't like, you know, I was making minimum wage or anything that decent paying job. And he says, Yeah, that was a huge gamble.  That's what he said to me. He says, Yeah, that was a huge gamble.  And I thought to myself, what is a gamble? What is a gamble? Is a gamble going and working for yourself and doing things that you want to do and depending on yourself to make things happen? Is that a gamble? Or is a gamble staying on your current job and doing what somebody else tells you to do and let them control your life? Which is the bigger gamble? What do you think is a bigger gamble? Now, you may say, Well, JR, at least I've got security. I've got this job and I've got security, right? This is a very secure job. I got news for you. There's no such thing as a secure job. Because whoever's running that company could make a mistake and they could go out of business.  Whoever's running that company could just not like you and want to mess with you and make your life miserable. You know, whoever's running that company could say, we're paying JR too much. We got to pay him less money. I've had that said to me too in my career where they'd say, Well, you earned too much money last month. And I was on a commission. And I'm like, Well, how do you earn too much money if you're on commission? You decided on the pay plan. They said, Yeah, we're going to change it. We've got to change it because you're making too much money. I actually heard that. So guys, let me go through the five steps.  The first step is to change your brain. That's it. This is the first step first of five steps is to change your brain. And here's what I mean by that. You need to start looking at things entirely differently. If you want to make it online, if you want to make it your own business, you've got to look at things differently. The first thing is to change your brain. And here's what I mean. You are not the job that you do right now.  Well, I mean, I am in the evening when I'm straight up the kitchen. But that was one of the first jobs I had. I was a dishwasher. And I also worked as an usher in a movie theater. I also drove a forklift at a pickle factory. I also bussed tables. I also waited tables. I also was a bartender. Am I any of those things? The answer is no, your digital marketer, JR, because that's what you're doing right now. You see too often, and this is why I say you got to change your brain.  It's a job. It's just something you selected to do right now.  You are not what you're currently doing. You're not that. That's just a thing that you're currently doing. I am not a dishwasher. I am not a forklift driver right now, right? But I've done those things. And I guess at the moment I was that thing, which you can change that, that can be changed in an instant. It can be changed.  You're not that thing. That thing is just what you're doing. So you've got to get that in your brain. When I told people, you know, this is number one, change your brain, we got four more. Okay, when I told people I was going to go online and sell stuff, whatever that stuff was, okay, they told me I was crazy. And they told me I was crazy for a lot of reasons. But the first reason was that I've never done it before.  Any job that you have right now that you didn't do before is the first time you did it. Okay, so it doesn't matter that you haven't done these things before, don't get wrapped up in thinking, well, I didn't do this before, so I won't be able to do it. That has nothing to do everything you do right now, you didn't do before everything. I don't care if it's walking and talking. At one point, you didn't do that. Okay, so you've got it, you've got to stop this, this beating yourself down and saying, Well, I haven't done that. So I can't do that. You've got to totally change your brain.   You know, your limitations are between about six inches right here. That's where your limitations are. And they could be changed. I remember an interview with Elon Musk and he started Space X. And he was being interviewed on 60 minutes. And the interviewer on 60 minutes and how in the world did you start a rocket company? How did you start this rocket company that has become one of the most successful space programs in the world? You're not a government. You're not a rocket scientist, the guy said to it. And Elon leaned over and he said, there's books. There's books, you can learn anything. You can learn anything. Now, once you've got your brain switched a little bit to where you're not saying to yourself, I am a car salesman, I am a cashier, I am a, you know, I don't know whatever your job is, an engineer, whatever it is, as soon as you stop doing that, the world opens up to you. As soon as you stop doing that, you start realizing all the other things you could be all the other things you could do. But the first thing you have to do is start to realize, start to realize that you are not your job. Okay, now we're going to get to number two. Number two, get started. Get started. Here's what happens with people. They plan and they plan and they plan and they take courses. Okay, they take courses, they take so many courses, they read so many books, they watch so many videos, they do all this stuff. Okay, but guess what? They don't get started. And why is that? Because they are looking for the thing that's going to work, right, which sounds reasonable, right? They look for the thing that works. When Elon must start his rocket company, he crashed some rockets. Okay, they crashed.  That's so horrible, your rockets crashed. And Elon said, No, it's a really good thing. You know, now we know what doesn't work. Now we know what doesn't work. You've got to get started. And you won't have a plan to get started.  And how are you going to do that when you don't even know what works yet? How are you going to do that? You can't do that. I had no clue what to sell, where to sell it, how I was going to make money, how I was going to market it. I didn't I didn't know how to type. Okay, I didn't even know how to type. And if I didn't know how to type, how in the world was I going to start an online business? Paul says having the right mindset is everything. Second is knowing what you want. Yeah, we're going to get to that too in this training too, Paul. So that's a good point that you just made. Take action and revise later. And that's another good statement. I like that too. And that's what I did. So what did I do? I said, well, I looked on eBay, and I looked on Amazon, and I found the number one selling product, I said, if I can just find the number one selling product, I can be successful at that. Okay, and the number one selling product was cell phone cases. This was in 2009. Cell phone cases was it. I mean, man, people were buying cell phone cases. So I got into selling cell phone cases, because I thought that would be it. And what happened was you see what happened was I was selling these cell phone cases, and I was making like 20, 30, 40 cents, every time I would sell one. And I would have to, you know, package it up, I would have to process the order, I would have to pay my fees to eBay or yeah, and I made 20 or 30 cents on each one. I wasn't making much money. And then what happened was, I would have to buy inventory, maybe 50 or 100 of these cell phone cases. And I would sell some of them. But then the other ones wouldn't sell because people would switch their phones, they would need a different kind of cell phone case. So I would just take those extra ones and I'd put it my walk-in closet.  And one day I got up and I opened the door to the walk-in closet and I couldn't get in the walk-in closet, because I had so much leftover inventory that did not sell, I couldn't get into the walk-in closet. And I'm scratching my head. I'm going, I got to get rid of some of the stuff. So I started selling those cell phone cases in bulk to other people who wanted to start a cell phone case business. Okay, so I would sell 50 or 100 of them in a big box and ship it out to them. And I lost money on them. I lost money on them. And I lost money on the whole venture. And people could say to me, well, you were a failure, JR. That's what happened to you. You started a business and you were a failure.  Okay, they would say, well, no, you're not a failure, you're successful. But that cell phone business got me to here. And that's what I want to tell you, you've got to get started because you don't know where it's going to lead you. Those cell phone cases led me to camping gear. And camping gear led me to selling this company's survival food. And when that company got screwed up, I started my own survival food company. And when that wasn't selling enough, I started this can meet company. And then that grew into me doing courses and that grew into me doing YouTube channels. And guys, you just got to get started. You got to get started, it's going to lead you in so many directions, you're going to learn so many new things, you're going to uncover things that you would never uncover. Now, that company that I work for has since been sold that automotive group. And some of the people I work with are still there. It's been 12 years, they're still there. And they're still complaining. And they're still saying I'm not making enough, if they would just up my pay a little bit, just a little bit, I don't need a whole lot more to get by, I just need a little bit. And some of the people have left, some of the people have died. People changed over the years, right? But they're still at the same place, even though they're internally changing, and externally, they're getting older, they're still doing the same thing, and they're letting some other person make all the decisions for them. Because they think this is security. It's not. I feel more secure every day now than I ever have in my life.  I do things that build my business. I know I can depend on me. I know that because I have taken care of myself for 12 years. I've done what it's taken to take care of myself. So you've got to get out of that mindset. Number one is change your mindset. You are not the job you're doing right now. You're not, you never have been. It's just something you selected to do for a while. What is Elon Musk? What is he? He's a creator, you would say. You would say, well, he can create anything. He can do anything. And you know why he can do so many things? Because he tries so many things. How many things have you tried? How many things have you tried to do? How many things have you failed at? If you haven't failed a lot, you aren't trying a lot. Because guess what? That is what happens when you start a business. As a matter of fact, that is my number three. Realize you're going to fail. Realize you're going to have failures. Realize things are going to go wrong. Now you say, well, I don't want to fail. And I'm going to laugh at that. I'm going to say, well, sorry, that is part of success, right? The athlete who can run, I don't know, a marathon in a set amount of time failed at that many times before. Time and time and time again, they failed at that. You know, some of the best, I don't know, home run hitters in the world, right? How many times do they fail at that? How many times they strike out? Most of the time. Most of the time. So number three, the big one here is, and this is a, you know, if you guys say, well, I just work out the technical things I need to do, don't tell me all this mindset stuff, the mindset stuff will get you to the technical stuff. But you've got to have the mindset first, because all the technical stuff in the world, if I teach you how to build a sales page and, you know, what products to sell and how much to sell them for and all that. And I give you all that. And you haven't changed your mindset and you never get started. And you don't realize that you're going to fail, which is number three, then you won't be successful. It's not going to work for you. It's not going to work for you guys. All of these things I'm telling you right now are crucial to being successful at anything, really being successful at anything. And guys, you just make you so the chat box there, Paul's really good about it. Some of you aren't so good about it. And I know you're here. Say hello, participate. Finding people to model is an easy way to get started and look at them from a tactics and strategy perspective. That's some technical stuff, Paul. But I think what he means is look around. They're successful people. Here's what I did. I looked around and I looked at people who are having success online. And I looked at them and I said, Huh, they're no different than me. They're no smarter than me. They're no better looking. Well, it's a lot of them better looking. But the point is they didn't have anything that I didn't have. Yeah, sure. Maybe they could type. So what? It's going to take me longer. I still can't type, by the way. But the point is I looked around and I said to myself, you know, if they could do it, I can too. I would love to hear the story on how you made the jump to becoming a manufacturer. The journey had to be interesting journey. Well, Paul, it was really simple. I actually was selling somebody else's product. It was another brand and they quit delivering and I got my account canceled at eBay and I had money taken out of my account and I ran into all kinds of difficulties.  I would have never come up with my own brand if I hadn't lost my eBay account. If I hadn't have not had things delivered, if I hadn't gotten screwed over by that company, I would have never, ever had my own brand. Stephen Davis, great presentation. Thank you so much Stephen. I would appreciate that. I really do. I thank you for participating. You don't even have to tell me good things if you don't want, but just participate. The participation is not for me. It's not for me. It's for you. If you participate, if you start right now, if you do something right now, it's going to help you. And doing something can be as simple as putting a comment in there. That's a simple start, but it's starting because here's what you're doing. You're participating in an online business, right? When you do that. I got a bounce. I have a great weekend looking for it. All right, Paul. We got a good crowd here today. So all of you guys pick up the slack from Paul, put a comment in there. This is going to help you. This is going to make you participate. This is the thing you need. Okay. This is the thing you need. So right now we're on realize you're going to fail. Realize you're going to fail. That's so important. Failure is good. Failure is great. Failure is awesome. Okay? It means that you tried something. If you never fail, that means you're not trying very hard. You're not stretching a whole lot. You know, when I go to the gym, if I can easily lift a weight or if you go to the gym and you can easily do five setups, you're not trying hard enough. You've got to try past what you can do because that's the only way you're going to grow. If you don't try to lift more weight than what you can currently lift, you'll never get stronger. It's not going to happen. It's just not going to happen. So you have to try these things. How did you develop the meat brand and did you start doing private label or jump straight into a plant? I didn't really start the meat brand. Here's what happened. I was selling freeze dried dehydrated foods and all the people selling my food said we need a protein. They started it. They said, hey, JR, this is what you need to do next. And I listened to them. I heard them. I said, oh, you want something else. Let me figure out how to do that. And then I figured out how to do that. But I got that input from people out there that was already selling my products. And here's the interesting thing. If I didn't start selling cell phone cases, which some people would look at and say you failed at, I would have never gotten to freeze dried foods or canned meats. It wouldn't have ever happened because I failed at these other things. I learned to do new things. When you start, guys, and that's what I that's part of what I told you today, you got to get started before you know what's going to be successful. When you do that, you are going to grow. Okay. You are going to learn new things. You're going to discover new things. You're going to get stronger and better at what you do. Never saw a book on how to make canned foods for a living. No, there is a book on that one. There's and it's not canned foods. It's a very specialized canned meat that we do. It's very special. We're the only ones in the country to do this. Some people will fake it and pretend to have the same thing. They don't. Nobody has the process we do. And that's proprietary, but it works really well. A lot of people buy it. Okay. Cheryl Dean Cornell. Hey, J. R. So what's the biggest thing out there now? Effort effort, put in forth the effort. You know, I was I was talking to my daughter-in-law the other day, and she has a bird called Sansa and the bird talks and she started a gosh, is it is a tick talk? No, Instagram account and the bird has thousands of followers now and Facebook contacted her and said, we want you to do reels and we'll pay you. And she made, I think, $12 or something in a day. And I said, Cheryl, my first sale was $10. And yesterday I made $62,518. $62,518. Now, $62,000 in a day, you may say, well, J. R., that's a lot of money. It's not. It's not because we've had days where over six figures. I've had days that are only five figures too. But I would have never gotten to that stage if I didn't put forth the effort. And it's not the product. It's not the product. Everybody's out there going, I want to find the right product. I want to find the right program to promote. I want to, it's not any of that. That's what I'm trying to teach you today in this training. What it is, is that you go out there and actually start doing something. And you're going to uncover all these things. See, if you don't go out there and get started, you can't look at the landscape and figure out what's going to work. It's impossible. If I hadn't failed at selling cell phone cases, then I wouldn't be able to figure out how to do the things I'm doing now. I had to fail at that first. And you're going to have to too. It's part of the growth. That's what you've got to do. And if you stay in a job because you think you are that job, right?  You're not that job. I was not a car person. I was not. I am a salesperson. I'll give you that one. I'm a sales person and I'm a marketing person, but I'm not any particular job no more than I was a forklift operator when I drove a forklift in Portsmouth Virginia at a pickle factory at Best Foods. That's what I did in college. I drove a pickle, a forklift at a pickle factory. My job was to these big trucks would come in with these big crates of cucumbers and I would have to forklift one of these crates and then drive it over to this conveyor belt and then tip it and dump it into this big bin and then we'd go up in this conveyor belt into the building and somehow miraculously they made pickles out of those. But I was not a forklift driver. I drove a forklift and they paid me for it. I washed dishes at Victoria Station restaurant and they paid me for it. But I was not a dishwasher. You are not your job. That was the first thing I told you in this training today change your frigging mindset.  They should care about their family. All they're doing is using you to get to their goals. That's all they're doing and there's nothing wrong with that because when you start your business you're going to hire people and you're going to pay them to help you get to your goals. That's how it works and people say well they should care about me more at this company. They should want me to make more money. They should understand that I have bills. I had a I had a person come in my office one day and they said I have five kids. I need more money. I said it's not my fault you had five kids. That doesn't mean the job is going to pay you more. And by the way Cheryl you know that person. So you look around the dealership with somebody who has a lot of kids and you're going to know who that is and they worked in finance. But that person said to me you need to pay me more because I have more bills than other people do. It doesn't work that way. It does work that way if you go out on your own and start your own business then it does work that way because you could say well I want to put forth more effort. I want to put more forth more effort because I have more bills. You could easily do that. OK. But you can't go to a job and do that. So the first one was change your mindset. The next one was get started and learn at the same time. And that's what I did. I learned right. And then number three was realize you failed. Number four is the next one. And I've only got five of these. Number four is a pretty important one I think. Number four and you can put it in the chat if you think you know what it is. But number four is what? What do you think number four is? It's decide what success is. Decide what success is and the second part of this realize it's going to change realize it's going to change when I quit that automotive route I had in my brain what success was. And I'm going to share it with you right now. Success to me was if I could make half of what I was making or running these car dealerships I would be happy because I hated my boss. I didn't like the way he treated me. I didn't like what was going on. I didn't like the way they treated customers. I didn't like any of that. So I decided what success was. Success to me was making a salary that would be equivalent to one half of what I made of the dealership. Now what happened? I ended up making more. I ended up some days I make more in a day that I used to make in an entire year and I made a good six figure salary which means some days I sell over six figures. That's not bad. I had one of my vendors the other day send me a P.O. for seventy three thousand dollars one P.O. Seventy three thousand dollars. I would have never gotten that P.O. Right. If if I hadn't sold some cell phone cases. Right. So it's getting started. It's not the hottest thing that's out there. It's not the biggest thing that's out there. It's none of that. It's not that at all. It's getting started realizing you're going to fail and you're going to learn things. That's what's going to happen. There is no secret key to this. It doesn't exist. Now every day my wife and I look at marketing. We're I mean we're all over marketing. We'll look at a sign and we'll say that's a bad sign. We'll look at a truck and we're like it doesn't say what they do. It is the name of their company. What's the point of that? It doesn't say what they do. We look at marketing all day long. We look at a menu in a restaurant. We see how they market their food. We look at a shopping center. We look at their signs and see how they market it because that's what we do every single day. We market stuff. We sell stuff. OK. And we try to sell the best stuff we can sell. Whether it's my training whether it's a book I've written whether it's my food products you know whether it's my inner circle what no matter what it is we try to sell the best stuff we possibly can. And that's something you got to do. That's something you got to do. So we're at number four right now if you're if you're playing along we're at number four. All right. And number four was decide what success is and my my idea of what success is has changed dramatically. Now I don't really look at money so much anymore. Though it is a real good indicator if you're doing the right things. Right. If you're making a lot of money you're probably doing a lot of the right stuff. OK. Unless you're doing unless you're cheating people doing stuff wrong and we're going to exclude that we're going to say you're an honest person. OK. Who wants to make money. So number one was change your mindset you are not your job. Number two was get started and learn at the same time which is what I did. Number three is realize you're going to fail and you will you will but that failure is going to help you find the good stuff. Number four is decide what success is and this will change. My idea of success is not to earn half of what my old salary is because I would be terrible now. I can imagine trying to live off that because I can go where I want now I can wear what I want. Right. I am in the house I want. OK.  I just don't. I have a deposit on the Tesla truck but I've been driving the same car for almost 10 years now. I don't care about it. It doesn't matter to me because sometimes I go to bad neighborhoods. You know because they have some really good food restaurants and I want to go there and you can't drive up in some Ferrari or Lamborghini. Can I buy one of those. Yeah. Yeah. I don't want to. I don't I don't need it to get get a girl or any of that. I think some people do that. They get cars. They get possessions to attract people. And I think that's the wrong way to go about it because think about who you're going to attract with a big gold watch or fancy car. Who you're going to attract. Somebody who wants your money. That's who you're going to attract. OK. So that doesn't matter to me so much. I will tell you a funny thing today. The neighborhood I've been there's some nice cars. There are some Lamborghinis and Ferraris and Bentley's and all those and there's these two Bentley's I see all the time and the glass in the Bentley's is totally dark and you can't see the person inside. And I said to my wife the other day I said what's the point. What's the point in having a car that looks like that. Right. What's the point in having a car that looks like that and nobody knows you're in it. I mean it can't really ride that much better. I've driven it of Rolls Royce. It doesn't ride that much better. The point of having a car like that is so people can see you right.  I mean if you just put it in your jewelry box and you don't wear it it doesn't matter right. When you're when you're buying these possessions guys when you're doing things fancy name brands Louis Vuitton this and all that stuff and I don't do any of that. But when you're doing that you're doing it because you want to feel good about who you are. And I'll tell you what makes you feel good about who you are accomplishing things doing things contributing helping others. That's what's going to make you feel good. And it's also sidelined. It's going to make you a lot of money. It's going to make you a lot of money. So I've been through four of them. I want to do it one more time. I'm going to give you the fifth one in just one second here. We're at 10 30. It's time for the fifth one. And it's a change of mindset. You're not your job. Get started and learn at the same time. Which is what I did. Realize you're going to failure or have failures and everybody does that successful. Every single person ever said I don't care who it is. They all have some sad stories. Decide what success is and this can change and you need to change what success is. And success can be money. It can be freedom. You know, I wanted freedom and I wanted a little bit of money but I wanted freedom more than I wanted money. I didn't start online business to make a whole lot of money. I mean, if I made a whole lot of money I'd be great.   Sometimes you aren't hungry when they want you to go to lunch. Sometimes you get hungry before they allow you to go to lunch. Is that what you want to continue doing? You got to ask yourself that question. Are you getting younger? I've never met anybody that was getting younger. Matter of fact, I had people and they would hold up a picture of themselves and they'd say, hey, this is a picture of me when I was younger. I'm like, all pictures of you are when you're younger. All pictures are. Okay, so we're gonna go to a number five right now. Number five, if you're keeping track we're at number five and I've reiterated with the first four are number five is what? What is number five? See if you can guess what number five is. Realistically, how much of a financial investment do you think it takes to get started? I started with $100 on my credit card. So I technically started with zero, zero. I have credit cards now that I could buy a house with, right? I never had credit cards like that before. Never in my life did it. But getting into doing stuff online. See, here's the thing about online guys and you may be missing the point. You may think that selling online is some kind of fad something different. This has been going on for years. People have been ordering from Sears and Robot catalog for over a hundred years now. I think they're out of business now. But the point is this is not a fad. This is how people shop now.  Then you're missing out because you're watching all these other people make money make millions of dollars. We have, I have millions and millions of dollars. It blows my mind. Sometimes I'll log into my website and I see how many millions of dollars went through it.  You know, I've got a little bit left. But the point is it doesn't take, it takes more effort than it does money. Money, if money could buy you a business you could just go out and buy a business that's really profitable.  When in fact, the average person doesn't realize this when you buy a franchise, you're less likely to be successful than if you start your own business without a franchise. Did you know that? You're less likely. Did you know that the average McDonald's owner only makes about $200,000 a year? Now that sounds like a lot of money to some of you but it's not. They have to invest millions to get it. They can take that same money, put it in the stock market and make it not even have to work, right? And if something goes wrong like their minimum wage goes up too high or something that wipes out most of their profits because if you've got eight, 10, 12, 15 employees and you up their wages $5 an hour times 10, 12 hours a day that can wipe out your profit. So buying a business is not the way to go. The number one thing I told you in the beginning was your mindset and how you changed how you think. You've got to change how you think this is the hardest thing I get across to people. I'm gonna give you number five now. I'm gonna give you number five and this is a big, big, big one. Continue to learn new things. Now you say, oh, J.R., I'll do that anyhow. I bet you don't. I bet you can't tell me what you learned new yesterday about marketing, about sales, about putting something online and making more profit. I bet you can't tell me that. I spend a lot of my time watching and reading new things. A lot of my time watching and reading new things and it gives me ideas. It gives me ideas that lets me go, oh, I could do this or oh, I could do that. Those things matter a lot. And guys, use that chat box while you can. I'm gonna be gone in a few minutes and you won't get a chance to ask a question. So make sure you use that chat box. Super important that you do that. These five things, guys, are the secret to quitting your job. I quit. I quit. Matter of fact, I remember the day I quit because I went into my boss and Jimmy, I'll just say Jimmy, and I said, I'm gonna quit. And he'd been threatening me. We don't have a good month. We're gonna have to put you in another position. We're gonna have to do it.    If you're really sick of it, listen to this video three or four times. They are not gonna change your future. It's up to you. They are not gonna make you secure. It's up to you. They're never gonna make you secure. They're never gonna care about you. They're never gonna want more for you. They're never gonna like your family more than they like their own. It's not gonna happen. It's unrealistic. It's just not gonna happen. You've gotta realize life ain't like that. And you can get angry about it. You can complain about it.  You can moan about it. Fancy Empress. I haven't seen you in a while. Good to see you. What's your most favorite way to advertise your products that actually work? Here's the deal. Here's the deal on advertising. It all works. You can do it right. And advertising online is like no other medium because you can test it. I can run it to certain audiences. So when we run ads online, which I'm not running any right now just because we have so much business I can't keep up with what I have. So I don't need to get more business because I'm running out of products. But when you advertise online, you don't run one ad. You run 20 or 50 ads, okay? Different ones to different audience. Then each one may go to 15, 20 different audiences. And the majority of those are gonna fail. So what I've done with my ads when I run 50 to 100 ads is I figured out which ones don't work. But some of them will work. And those some that do work is the ones that I put more money into and then I cancel all the other ones. So you can't do that if you're putting an ad in the newspaper of Bill Shepard. You can't do that. You don't know if it worked or not. But online you'll know because you're targeting audiences. You're targeting ages. You're targeting demographics. And when you target all those things, some of them don't work and you cancel out those things and you continue to spend money on the things that do work. That's how you do advertising. Unfortunately, most people don't advertise that way. They say, I'm gonna spend $100 a day on this one ad and they run that one ad. That one ad doesn't work. And they're like, oh, it doesn't work. Advertising doesn't work. That's not how you do it online. You gotta run a whole bunch of ads and spend maybe $2 or $3 on each one. And you'll figure out ones that work or ones that don't work. And it's a simple process. It really is. And that's what I would say as far as advertising goes. I'm getting some good comments in here. Aim into that, Cheryl. Very nice. I used to get alerts to your morning videos but lately I haven't been getting them. Oh no, Richard, let me check and see if you're still tagged and everything. I'll make sure that you're still tagged. Richard's my buddy in real estate, done very well in real estate and is able to travel the world and do what he wants if we meet up every now and then. Good to see you there, Richard. The alert to all is selected. I'll check that. Maybe you're not tagged. I don't know what it is. I don't know, it's weird. Do you have your, what do you call it? Notifications on YouTube turned on because that's something that, have you used digital billboards? Digital billboards. Not quite sure what you mean by that. There's so many acronyms and names for stuff. Fancy Empress, if you would put in there exactly what you mean there and I can answer that. And I'll tell you the best way, the best way to do advertising is to give free content, is to write a blog, is to do videos, is to do free training, to just give to people. Just give and don't expect anything back. And don't look for your other stuff. I had that all the time. I have people that watch my videos for three or four years and they'll join one of my memberships for 500 bucks a month or 200 bucks a month or 27 dollars a month or they'll buy a thousand dollar course because I'm out here doing free stuff all the time. I think on this channel I've got, I don't know, 1,300 videos, something like that. This, you would say, well, this isn't making you any money, J.R., you're just giving free information. But it does because people learn about me and they learn who I am and what's going on. Let's see here. I saw an ad marketing billboards but they are digital. Yeah, anytime somebody advertising, advertising, I kind of shy away from it. Google never runs ads on their ads. I don't think, I don't think they do that because the stuff works and they don't need to. So I would say I would stay away from that. But I would tell you that the number one best way to advertise is to give people free stuff. Let's say you're selling some type of makeup. Do makeup tutorials. Let's say that you're trying to sell an exercise program. Do free videos on workouts. There's so many ways you could go about doing this guys. It really is. LOL, good tip. Yeah, but they're trying to advertise their own stuff. They probably don't know anybody advertising. So that's what I got through it today. I do want to reiterate these things real quick. For those of you who came in late, you didn't hear them. There's only five steps to this. Five steps, guys. Change your mindset. You are not your job. Think about that. Let that sink in.  That's just what you chose to get up and go do every single day, right? Get started at the same time, learn. If you don't know where to get started, throw a rock. Wherever it lands, start there. But damn it, start.  And they still are dissatisfied but they still get up every day and go do the same thing. Makes no sense to me. If you're not satisfied with something, why do you keep doing it over and over and over? Think about that. Number three, realize you will fail it. You're gonna have failures, they're good. Deal with it, okay? Toughen up, buttercup. You're gonna have some failures. Number four, decide what success is and realize you're gonna need to change it. Your idea of success could change over time, right? My idea of success has changed over time. My money goals are bigger nowadays. You know, I want six figure days. That's what I want, six figure days. I used to want a six figure a year. I used to think that would be good. And then the last thing is continue to learn. This stuff moves fast. Don't let that scare you that it moves fast. Too many people say, oh my gosh, it's so scary, everything's moving so fast. Just move along with it. Jump in the river and keep going, okay? And if you jump in there and keep going, you're gonna learn new stuff.  That's the stuff that matters. Let's see here, what else we got in here? Including me. Well, Cheryl, stop it.  Start something. When you start something and you get a little bit of success, what's gonna happen is it's gonna fuel you to do more. That's what happened with me. I sold something and I made $10. I was excited as hell. People may look at me and say, well, you're insane, $10 is nothing. Really? Well, six figure days or something and that's how I got here. That's how I got here by doing those things. 15 years and still using your script. Cheryl was a person that worked for me guys, if you don't know, in the automotive industry and we developed certain things that worked and glad you're still using it, but stop. Go do something else now. Go do something else. Repeat number two, please. Yes, number two. Let me get to number two here. And I had them in order.  Get started and learn at the same time. I got started by selling cell phone cases on eBay and by doing that, I learned what not to do and what to do. I learned two different things, okay? These things work guys. Google my name, right? Watch some of my videos. I'm not BSing yet, okay? If you want to make money, then you wanna listen to one of these people to tell you you can only work four hours a week. You're gonna put forth any effort. Just give them some money.  You're gonna have to put forth an effort. I had somebody one day who bought one of my courses and said, I feel so good now. I know I'm gonna be successful. I bought your course. I said, that's no, no. That's not gonna make you successful. What's gonna make you successful is using the course and applying what it teaches you. The course is not gonna make you successful. I can hand that course out to 1,000 people and I bet you 10 of them would be successful. What happened to the others? They never did anything. That's the biggest problem. People don't do anything. Go do something, guys. Apply this, don't wait. You heard this training today. Go do something today. Why not do it today? Why not? Now, some people will say, well, you don't always get good results. Right now you've got eight people watching you. It doesn't matter to me. I don't care. See, that doesn't offend me. It doesn't hurt my feelings because afterwards hundreds will see this. Maybe thousands. Maybe they won't. I don't care. I'm trying to help you guys, okay?  That's not my goal. My goal, my goal's changed. Remember my goal's changed? I said my goal's changed. My goal is to teach other people how to do this now. My goal now is to motivate other people to do the same thing I'm doing. That's my goals now. What's your goals?  Some of you will.   You guys have a great day. I gotta head out to the doctor's appointment at lunch and man, I really appreciate you being here. I appreciate all your comments. If you like this, put a comment below. I know some of you don't watch this live and I get that.  You may be watching the evening, the weekend, whatever. Still put your comments in there. Put your questions in there. I come back and answer them. I answer 100% of these comments. It's hard to do. I get a lot of them. I have 1,300 videos and people put comments on them and I still come back and answer them and it's me answering them, not somebody else. If you want more information on my training, it will be in the description when this video has been uploaded to YouTube. So you can look down there. You can grab that stuff if you want. I do have affiliate links there. If you're looking for any of the equipment I use, any of that kind of stuff, you'll find that in the description below. I really appreciate you guys being here. I appreciate you participating. I thank you so much. This channel would be nothing without you. So make sure you give it a thumbs up. Make sure you subscribe. Make sure you ring the bell. Turn on all bell notifications so you're notified each and every time I go live. Guys, have a great day and I'll talk to you real soon. Have a good day. Bye-bye.


Hey, welcome everybody welcome to the live stream. How you doing? How you doing? I'm Jim. Let's see How's everything going? Can you hear me? Okay? Can you see me? Okay? How's everything going? It's Sunday night. We're gonna run through a couple of things run some tests on some things that I had a bad screen the other day and There's so many things that can go wrong Going live between it could be as simple as a wire you went bad in which I think happened But you know, you go crazy looking at your cameras and your microphones and your software and your computer and your laptop And it's just there's too many variables to try and narrow down what the problem was But I think I narrow it down to my my connection to the camera and the cable so hopefully that fixed that out, but We're live on Amazon.  Hey, we got a nice camera. We got a nice comment. Thank you Levi for a nice setup Thank you very much appreciate that Yeah, so we're working on it now there's Levi's comment right there down here on the on the on the screen, right? That's pretty cool. So now when you when you chat It's gonna go on there now. What's also is gonna happen is up here. This is the snake, right?  So right now Levi doesn't have a doesn't have a profile picture. So it's just a blank picture there, but Somebody puts on see how I'm right behind them on there because I said nice I said hi at the beginning. So, you know, this the snake's gonna go around and whoever makes the next comment will be the head of the snake and when we get I think 80 comments the whole screen will be all the way around and Whoever's that last person is the winner. Okay, whoever's that last person is the winner How about that? So we're gonna go through a couple of things Like I said, I'm checking out my stream. I'm checking out the camera and everything making sure everything is working, right? This is something I use every day. It was sent to me for free or everything that in the stream today was sent to me to review for free I work for an agency called the ratio and they have a bunch of brands under them They send out samples for people to review now. I'm a service technician in my day job I go and go to people's houses and provide service A lot of times I need a flashlight and it's nice to have a little pen light and this comes in a set of two It's a metal frame very very sturdy things What's not gonna fall?   I take this with me. It's in my pocket I need a light, you know quick small light to check something out And I just look and if I need to go back to my truck to get a bigger light You know, at least I have at my disposal right there when I'm for now first day I have a light in case I need it This thing comes in very handy and it comes in a two-pack now It's a triple-a batteries come to doesn't come with batteries, but it takes two triple-a batteries to make this thing work And I've had about a month now and I use it pretty much every day and the batteries last pretty pretty good I bought some rechargeable batteries and I still have yet to have to change them I'm not using this constantly. I go check something out, right and then turn it off You know, that's it doesn't take much, but this is a good light I would recommend it highly like I said, I use it every day I carry it with me every day in my pocket and there's two of them So now I keep one at home and I got one with me at work and you know God forbid I leave one I'll lose one somewhere. I have an I have a backup to great that they give you two And the price of the thing is not to be believed now. Hey now if I go like this So here's the thing All right, there we go. Okay, so there it is and it's 2394 of the gear light s100 LED. So now When I put this up on the stream the people on on Facebook and the people on YouTube can now see it right so now and they can also and now it's gonna Post the link in the chat on YouTube and Facebook so that you're curious and you want to see what that is You can click the link and go on over to Amazon and and check it out This is a great little software that I'm using. This is a be live that I'm using and so far You've got the snake running around the bottom You got the comments that get highlighted here and you got now you got the products in the in the carousel being being shown on Facebook and YouTube with links, okay that people can click and come on over to Amazon. It's great It's awesome. This is a great software works really well when it works and it works it so far. It's working really good Gear light. Okay. Now. They sent me a couple of lights. They sent me this other one this thing. I really like let's Go down to the next thing in the carousel This is what you gotta do. I got too many Things going on again. Okay, so you gotta you gotta you gotta have the iPad going so there you go now I got Do I have to switch this over to? Boom There we go Gear light. All right, so the gear light headlamp, okay It's getting dark now early right you want to take a garbage out you want to walk the dog You want to go jogging you want to pick the kids up at the school bus at 4 30. It's starting to get dark Okay, you wear this. Okay. It's got if we hold it long It's got the red light. Okay, so now people can see you when you're walking. Okay, and it's got different settings I think it blinks They're blinks. Okay, and so the people will see you I think that's the SOS blink It's got a couple of different blinks they're going right and if you won't press it again It'll come back on to the white light to the bright light So you can see we don't any angles down so you can see what you're doing and you know keep your hands free headlights headlamps are good Because it keeps both your hands free you can actually work and use both your head You don't have to hold the flashlight or you didn't you don't have to have someone hold the flashlight for you You've got you got the light right there, but I think that it's worth it this time of year You know you're walking the dog or you're picking up the kids up from the school bus Like I said or you know you're jogging, you know, whatever you're doing and you know You need that red light just to let them know that you're there because you know even if you wearing bright clothes you're jogging around and You know it comes in handy. It's a good thing to have so that's the gear light again This was also sent to me for free to review the the it's lightweight. It's adjustable the strap is comfortable Okay, it's not like it's lightweight. So it's not like something that's holding it down when you're wearing it You know, it's it's pretty cool. It's just like wearing a regular headband like a sweat band you know the old sweat bands used to wear and Yeah, pretty cool pretty good item And it comes in handy if you you know like I said if you work in person and you're like me and You're outside doing something around the house now It's 435 o'clock you're taking the garbage out or you know doing whatever you're doing around the garden You know now you have something because now it's getting dark earlier It's gonna start it's by the time the winter is in full force. It'll be darker for 34 o'clock, right? So you need these kind of lights for that time of day for sure And the gear lights a good company and then of course they send you everything. It's it's always two of them It's two of those great stuff. It's great stuff. Oh Java junkie And the Java junkie I'll be drinking coffee all day long so that's the way it is. I'm sorry if you don't like it but who cares The next item in the stream, we're gonna run right through This thing is another one best seller on Amazon. Okay, catchy insect flying insect Trap okay, I'm gonna take it out. I might plug this in for you. It's got a blue light on the top This thing is great because no insecticides. Okay. There's no insecticides involved. That's what everybody wants today They want a chemical free bug control. So this has little blue boards here Okay, a little blue boards catchy boards, right? The cord put this out of the way The catchy Put that there so you can see it. All right the catchy, right? Let me see if the cord will reach Let me tell you show you how to put the you put The glue board down in here you put one of these it comes in a packet of ten of them So you put one of them down in there, right?  All right Young but So now it's got a blue light The blue light attracts the bugs to see the blue light in there, right? Blue lights tracks the bugs Then there's a fan in here that sucks them down into the glue board Okay, pretty cool and you put this in the dark corner in the house or around your patio Or your screen room or wherever it is and you put a nice quiet nice dark place The blue light will attract the flying insects right to it. This thing's great Like I said, it's a number one bestseller on Amazon and this thing is flying up the shelves No chemicals, right? That's what you only got a like about it. There's no chemicals involved sticky trap I mean you're gonna have to clean the trap, you know and do the trap every once in a while, but you know Okay, so we're gonna put this away Catchy indoor insect. It's a flying insect trap and it works really well. Obviously.  So here's something that we put in the man cave This is the the giggle and go magnetic dartboard. Okay. I got it hanging up right here We're I'll tell you what we're gonna have to hide this so you can see it There it is. So there it is right up on the wall. Okay, and On the back it has the regular target so you can do target practice So you you want to get your groups together in tight groups and then you can start playing the game Darts, you know, you got to hit 320 319 318 317s and then the three bullseyes, right and this The magnets a nice magnets and of course It never never never sticks with me throw it. Never does Bullseye couldn't do that again Okay, but when I guess when you're standing up too close, you're throwing it too hard It doesn't stick when I step back it sticks. They stick every time I play with it from over there all the time And it works really good. See I got a bullseye. It tells you how to do it all the time Hey, hey gizmo see it. How you doing gizmo? Welcome to the stream See how things where we popped in on a Sunday to see I think that I had a bad wire and I changed cameras and hopefully the streams a little better It's not it's not jittery or a clunky or freezing up or whatever, you know, so we're gonna go through a couple of things quickly just to Check it out. I'm gonna go back and check it out later and check it out. See how it is. Okay, because you know It's live so you got the only way to figure it out is to just do it right because it practicing it It's not live so Of course, I didn't shave for the occasion the next item was share that again The next item I have in there is Very cool gift item. Okay. Now, you know, it's time. It's time to start buying gifts for people around you, right? This is a really cool Cheap gift not expensive. It's not cheap. It's not cheap. It's not expensive. This is mixology and craft. These are the Whiskey stones, okay, whiskey stones now if you have anybody on your Christmas list that Is likes whiskey like scotch. They're they're into that, you know, the old scotch They don't want to water down their drinks, so they don't want to put ice cubes in it So these are the whiskey stones. I'm gonna open up and show you a really cool little Comes in a little tray Right there are granite stones. Okay They are made a natural machine polished granite Right and you put them in the freezer and they get cold and they drop these into their drinks into the whiskey To keep the whiskey cold without watering it down. Okay, so if you have anybody on your Christmas list That's into whiskey scotch, you know and and and doing it what they call neat, you know pure no water They don't want to water it down with ice. This is a great gift at the price, you know You got a boss. You got a teacher. You got somebody like that. Um, this is a really good gift It's a thoughtful gift. You know, you're thinking about them and and it's really It's a really great price for a gift for for somebody is They're gonna like it. It's something they're gonna like. It's not something that's gonna go. They're gonna go I you know another BS gift from somebody this is gonna be cool even even somebody that Doesn't isn't a big whiskey drinker who maybe occasionally drinks whiskey Would be interested would be an interesting gift for them definitely be an interesting gift for them Hey, this dog is this here too Well, you know, I'm thinking I did I thinking I did it was a bed wire bed bed Either the bed wire the bed camera, so I switched both and we're in business So let me know what you think how's the light? I think the light is a little harsh I'm not sure I haven't bounced it really good But you know, it's live. We'll see how it goes We got some music in the background. I was getting bagged also By YouTube for copyright because I was playing some jazz music Even though the thing was freezing the music was playing and so they begged me for some copyrights Which I'm so I'm gonna have to figure out some some way to get some music going because I'm using all my other stuff So I can't play music, so I'm trying to use my phone as a background and we'll figure it out We'll figure it out by Tuesday But that's a really cool gift mixology and craft, okay Now you see how the snake is going now We got people to make comments and they're gonna be the head of the snake Right, they're gonna be the head of the snake now if I go over here. I can show comments now. There you go, right? Stargazer just Made a comment. She's the head of the snake and there she goes and she says she commented I got it all worked out seems like I have right seems like I got it worked out. We'll see how it goes The next item in the stream and it's gonna be the last item today because I'm told you I'm burning through stuff pretty quickly It's also from xology craft. It's a good gift for Anybody who has a home bar, you know back bar. They something like that that they're gonna put on On display, you know guys men that have man caves take pride in their bar and this is something it's a cool piece to have on there It's got an engraved mixing Okay, it's It's got the cap on there so you can pour this stuff out. It's got the thing so you can do the little shake a runny, you know It's got this This is mixology and craft on it really cool These things these are these are posipore is these things go into your bottle into your whiskey bottle And just when you dump it out, it just gives you an exact shot So, you know, you don't have to use your shot list you can put this in, you know in the bottle And just turn it upside down and they'll give you an exact shot Now here is also it's a double shot on one side and a single shot on the other side for Measuring for mixed drinks, right? You put that in there. I think goes right there But this is a masher for I'm not really sure what garlic or whatever. Okay? You got your you got your nice spoon for your cocktails, right? It goes over here right You've got this here for your strainer goes right in there You got your ice Graver and your ice graver says mixology and craft right on it to graves and that goes right in there, right? And then this goes in here and then I got the corkscrew left as well I don't know where the corkscrew goes maybe nowhere. Maybe it goes underneath, but so but that's it That's a pretty cool thing. Let me hide that comment so you can see it All right This I'll slide it back a little bit So you can see it better. All right, so there it is. That's pretty cool gift For somebody that has one of those bars in their house in their basement their man cave man cave, right? Everybody has a man cave, right? My man cave is the studio. This is not really a man cave, but It's where I hang out so pretty cool gift to mixology and craft so I mean It's time to start thinking about getting people gifts and you know some people hard like I said bosses, you know uncles You know friends people that you know coaches people that you know teachers people that have Man caves. This is a perfect item for that. So I'm gonna leave that there with you Okay, that's the mixology and craft again Everything today that I showed you it was said to me for free to review Give my honest opinion on now I think this is a really cool gift.  I'm not a big drinker. I'm not a drinker at all. As a matter of fact and But I think this is really cool, so I mean it's Without a doubt and of course the whiskey stones really cool as well also by mixology and craft a really cool gift idea for You know your your boss or your teacher or your coach or somebody like that, okay Your uncle your grandfather, you know somebody like that. Okay, um really cool And that's everything in the screen now, what time is it we went through it's only been about half hour Maybe something like that me we see now. It's only been about 20 minutes So that's how long it takes to go through six items is 20 minutes So we're gonna come back on Tuesday Tuesday 8 o'clock. We're gonna go live again Tuesday 8 o'clock I think this worked out pretty good. I think I think the equipment is working out the computer I was afraid it was my laptop that was causing the problem Which it shouldn't have been because everything's in the cloud in the cloud but You know it is an old laptop and I I wiped a clean factory reset to try and get it to speed up a little bit and you know But that's what it is. So That's tonight's stream. I will see you on Tuesday 8 o'clock. Let me see if I can do this without messing it up


Welcome back to our lecture series, Math 4230, Abstract Outdoor 2 for students at Southern Utah University. As usual, I'll be your professor today, Dr. Andrew Missildine. So in lecture 21, we're ready to get a pretty important theorem that we've been building up towards for quite a while now. In fact, what we're going to prove in this video is that if D is a unique factorization domain, which remember a unique factorization domain means that it's first and foremost an integral domain for which every non-zero non-unit elements in the domain has a unique factorization into prime elements. Of course, in a UFD, prime elements and irreducible elements are one of the same thing. So if you have a unique factorization domain D, then the polynomial ring D adjoin X is likewise a unique factorization domain. We've mentioned previously that a lot of properties of the ring D can be carried over to the polynomial ring as well. So if D has unity, then DX has unity. If D is commutative, then DX is commutative. We've seen previously if D was a domain, then DX is a domain. And we kind of got stuck there for a while. We were able to show that if F was a field, then F adjoin X is a Euclidean domain, which then implies it's a principal ideal domain and a unique factorization domain. But as of course, we've been interested in factorizations of polynomials in, well, we've been interested in factorizations in integral domains to begin with. So UFDs are the places to be. But how about factorizations of polynomials? We learned from Gauss's lemma that factorizations of polynomials over UFD coincide with factorizations of polynomials over the field of fractions. And since the the field of fractions is necessarily a field, F adjoin X in that situation is going to be a Euclidean domain. In particular, it's a unique factorization domain. And so we can push that back on to D. So really, this is going to be a consequence of Gauss's lemma here. So to be a unique factorization domain, we have to prove that every nonzero, non-unit element of DX has a unique factorization. So we have to prove the factorization exists and that it's in fact unique. So we don't have to worry about zero because you don't get unique factorization for zero. We have to also worry about units, right? Now, we know from previous work that if there's any units in DX, they actually belong to D themselves. That is the only units in a polynomial ring, they would have to have been coefficients, constant polynomials to begin with. So any unit in DX actually already belongs to D. And so in particular, if F is a constant polynomial, then it's really just an element of D in which case it has a unique factorization, unless it's a unit, but whatever, we don't have to worry about that. So the constant polynomials were good. So we have to consider a polynomial F whose degree is strictly greater than zero. That is, it's positive. And we know it can't be units. So with such a polynomial, does it have a unique factorization? Well, like I mentioned earlier, the field of fractions is going to be relevant in this conversation because the field of fractions, which itself is a unique factorization domain because it's a principal ideal domain because it's a Euclidean domain, F of X there. We know that since F of X is not a unit, it's clearly not zero, it does have a prime factorization inside of F a joint X. So let's say this is our factorization. F can be factored as P1X times P2X times P3X all the way up to PNX, for which each of these polynomials are going to be irreducible elements of F a joint X. Now this is where Gauss's limit comes into play here. If we have a factorization of F over the fraction field, then we can, without the loss of generality, suppose that each and every one of these polynomials Pi are actually polynomials inside of DX. But they might not necessarily be irreducible anymore over DX as they were over FX. So that's the thing we have to be concerned about, which we could factor out their content. It could be, because after all, the content of a polynomial is going to be an element of D, which every element of D, except for zero, is a unit inside of F. So with regard to the factorization in F a joint X, it doesn't care about content, because content is always a unit. But in D, that content might not be a unit. And so factor the content out of F, let's say the content is A. We may, without the loss of generality, assume that each and every one of these polynomials P1, P2 up to Pn are primitive polynomials. That is, their content is trivial, which remember the content is the GCD of all of the coefficients. So we have some factor A in front. So we have these, we have these polynomials P1 through Pn, which are primitive polynomials inside of DX. And we know they're irreducible over FX, and we factor out the content. So that's where we are right now. Now, as PIX is primitive in DX, we have seen that PIX is necessarily going to be irreducible in DX, if and only if it's irreducible. Did I say that one right? These polynomials are going to irreducible in DX, if and only if they're irreducible in FX, because of the primitivity statement there. Because after all, if PI had some factorization in DX, say we factored into some type of, you know, some other polynomial, some Q1 times Q2 or something like this, if this was a factorization in DX, whoops, into DX, then this would be a factorization inside of FX, which PIX was irreducible there. So one of these would have to be a unit. And therefore, one of these elements would have to have been, would have to have belonged to the domain D, for which if we could factor out some non-unit element away from PI right here, that means it wouldn't have been primitive. So the primitivity of a polynomial in DX means it's irreducible in DX, if and only if it's irreducible in FX. So okay, so we can then say that each and every one of these polynomials PIX is irreducible. We know it's irreducible in FX, so therefore it's going to be irreducible in DX, because these are in fact primitive polynomials. Now, as D is a unique factorization domain, the content of the polynomial has a unique factorization. So A can factor into A1, A2, A3, up to AK, right? And so these are going to be irreducible factors inside of D. They're constant terms, so we can't factor them anymore in DX either. Therefore, the polynomial FX does have a factorization into primes, into irreducible elements. You factor the content, you factor the polynomial in FX, and so this gives us a prime factorization. That's the first step to be a unique factorization domain. Every non-zero non-unit element needs a factorization. Why is it unique? Well, that's what we're going to do on the next slide right here. Why are these factorizations unique? So suppose that F, the same polynomial here, has two factorizations inside of DX right here, right? So one of the factorizations was the one we saw a moment ago. So you factor the content A1 through AK, you factor the polynomial P1 through PNK, for which we can assume that each and every one of these polynomials is irreducible in DX. Therefore, it's primitive in DX, and then the content is also factored into its prime divisors inside of D. We're going to do the same thing with B right here, right? You took out all of its content. Therefore, the Qs are each primitive polynomials, and the content can also be factored uniquely like so. Each of these polynomials, P1, P2 through PN, and Q1, Q2 through QM, we can assume that these are proper polynomials. That is, they're non-constant polynomials. We know that none of their degrees are zero. Again, they're non-constant. So these polynomials, Pi and Qj, they are proper polynomials. They're degrees greater than zero. And the numbers A through the As and the Bs, these are elements of the domain D. So they're constant polynomials, their degrees equal to zero. So that's the factorization we have there. And again, we also know that the P's and the Q's are primitive polynomials over DX, because they're irreducible. Now, again, that's what I said just right there. Since they're irreducible, they were primitive. Now, as such, Pi X and Qi, or Qj X have to be irreducible over FX as well, because again, this is Gauss's lemma. The factorization over DX is the same as the factorization over FX, essentially. I mean, there are certainly other factorizations you can do in FX, but it can always be pushed back onto DX. And so by Gauss's lemma, we know these polynomials, they're primitive and they're irreducible in the Euclidean domain FX. Okay, so let's set A just to be the content here and B to be the content of the second factorization. Then in particular, these are units inside of FX because they're neither one of them is zero, because that would imply FX was zero. They're constant polynomials, those are all units inside of FX join X. So then the above factorizations of F have to be unique, because FX join X, we've proven, is a Euclidean domain, so therefore it is a unique factorization domain. So when we look at this up here, if we just call this thing right here A and this thing right here B, these two factorizations, because A and B are just units here, this factorization of F inside of FX join X, we have unique factorization there. So there's a one-to-one correspondence between the factors, the irreducible factors of the P's and the irreducible factors involved with the Q's. So we're going to get things like N equals M and we can then say without the loss of generality that P1 is an associate to Q1, P2 is an associate to Q2 all the way down, so that PN is an associate of QN like so. Because again, we have unique factorization in that situation. All right, so where are we now here in our writing? Now as each of these polynomials PI and QI were primitive in DX, it actually holds that they must have been equal to each other. Because if there are associates, if P1 was an associate to Q1 X here, that means we can time something, we have a unit so that P1 X times a unit times Q1 X, we have equality in that situation, where of course a unit would necessarily have to be a constant polynomial. So as this element U is an element of D, we can basically kick this thing out here and so we can just assume that the Q's and the J's are actually equal to each other, canceling these things out because DX is in fact a domain, it then boils down to the A's versus the B's, right? So we then have A equals B, for which yeah, we push this U over here into this part of the factorization. So these are elements, these are these elements A equals B is inside of a unique factorization domain. So this is two different factorizations of the same element, A and B are the same element. So by uniqueness, we're going to have to have that these factorizations are the same, they have the same number of factors, K equals L, and there's this one-to-one correspondence between association in that situation, and this improves that we have a unique factorization of FX here. So therefore, the polynomial ring D adjoin X is in fact a unique factorization domain. Now it's worthy to note that if we take the previous theorem and apply induction to it, we get a stronger corollary. For example, if D is a unique factorization domain, then D adjoin any number of indeterminants will likewise be a unique factorization domain. And why does this follow by induction? Well, this ring can be written as DX adjoin 1, X2, all the way up to X in minus 1, and you can think of that as the coefficient ring when you adjoin on a new variable. So if you have it in the first step, then you have it in the second step, the third step, the fourth step, it follows by induction. So if with any finite number of indeterminants adjoin to a unique factorization domain, you still have a UFD. So this will include Z adjoin X, a field adjoin X, Y, a field adjoin three variables, or field adjoin four variables, you get the idea. These are all going to be unique factorization domains, but they're not going to be principal ideal domains, right? Z adjoin X has an ideal to join X, that is, you have two an ideal generated by them. That's not an ideal. Excuse me, it is an ideal, it's not a principal ideal, and therefore ZX is not a principal ideal domain. F adjoin two variables X and Y, you can take the ideal generated by the two variables X and Y, that's not going to be a principal ideal. And so these are good ways to construct unique factorization domains that are not principal ideal domains.


EA just dropped a new event Yo, what's going on leaf nation has to leave her back again and welcome back to the channel today We are back with a new event and a brand new pack opening where we hope we can pull something Because the bank account on on NHL 22 is hurting a little bit So look in here. We have fantasy hockey Evo So I know I know you guys are probably familiar with this So I'm gonna go over this very quickly These cards that are out right now plus one for every goal they score plus two for every goal Scored for a defenseman plus one overall for every win and shuttle or shuttle for a goaltender Customizable synergy so added at 95 overall maximum upgrade is a 99 and it only counts for the regular season in the NHL SHL Liga games. That is it.  We got these out as well 84 Riley 84 Sergicev 83 Monji upon a 80 Kessel you see the rest there some pretty good cards that are out We have 5800 points available looking at the sets I did do one of them and you guys should do it before the set expires It might have been expired by the time this video goes out You trade in 30 random goal players for a random 83 to 87 overall player Items so we have one of those to open we're hoping for the best and then we got points to open So we're gonna kick it off with this 83 to 87 overall player choice pack. I Want to see that purple yeah, give me a purple here. Come on or anything higher than an 84 would be great We get 83 Tarasenko. Okay my luck. That's okay. Get the bad luck out of the way. All right looking at the packs here I purposely calculated it where we can open up one of the fantasy hockey evil starter packs one of the weeks and week fantasy hockey evil prospect packs and then Max out on these packs. So we'll start off with this. We get a random week one fantasy player hockey item Who's it gonna be? Give me something good here. It's Philip Tomasito. It's our first card Which is an ideal. I would have liked to hype it up a little bit. Not too bad I'm not sure where he plays on Nashville. Hopefully you can get some upgrades He's already at an 81 so possibly you can go up higher. Let's see what else we have in this pack here Hopefully something else. We do need low rate of leaf players to finish the leaf collection So that'd be greatly appreciated. We get a jumbo Joe Thornton and 300 coins, but hey, you know what not a bad overall I would have liked the Michael Bunting or a Riley just cuz they're they're my Leafs It would be nice, but it's okay. So we're gonna go here. We got 182 plus. We'll open this one up next Let's see what we can get here. We got a pretty good chance at an 86 plus it showed So let's see what we can get in this pack. Something big would be huge. This is untradable by the way So that's okay at Colton's Sizzens. Come on something good It's been a while since I pulled something on this account David Perron Zach Wrenski 82 overalls, which is decent But not too good. We do get a power-up collectible, which is huge I do have an x-factor obi that I need to upgrade and we get a mat do Shane when he has an 86 master set Player out right now. So that one that one hurts a little bit not gonna lie All right, so we opened up those we are gonna move on to the NHL player packs And then we'll save the jumbo NHL player packs or whatever they were cuz they're better So here we go Bench Rock not ideal. Come on Robert Hague Like I said, if you're gonna give me low rate of players, give me some Leaf players. Please and thank you Cody glass Zemson Gergensen's Daniel Sprung Shea Theodore Victor Olives in oh my goodness and a Jacob Ron These packs are not giving out right now EA juice my packs, please So we have four 80 plus is in here. What are the odds actually we get a 6.6% chance at an 86 plus That ain't the greatest if we're gonna be honest with each other here boys But you just never know man. You just never know Kevin Fiala is an ideal 85 prime time Alexander. I don't know why I said Alexander Alex Petrangelo That's not a bad card. He might actually make the team I might just sell them to be honest to get some coinage He's got bombarded, which isn't a bad synergy. Not a bad card. It's an 85 overall card We won't complain. We got a Wayne Simmons not the low rate of leaf player. I need I need a 74 to 79 Marcus Felino Jordan Stahl anything else Justin Schultz and That is about it, but hey, we'll take an 85 Petrangelo. It's not a purple, but it is an 85 We'll take it. All right, we got one more of these left. Can we top an 85 out of these packs? This is our last chance to see if we can EA do your thing John Hayden not ideal Michael Furlan. Come on I'm hyped about a Michael Hutchinson pull. We need like two more leaf players, and I'm done the leaf collection That's huge. We'll take a Michael Hutchinson Chris Drager Eric Johnson Ty Smith Your Jordan Kyru Brian little Ben Bishop and a Dante Fabro. Okay. Well, we were hyped about the Michael Hutchinson Sorry and we are down to the Jumbo premium players pack 20 items all gold players with at least 580 plus overall players Come on EA. Show me the money. What what what do we have here 8% chance at an 86 plus? 8% chance let's see if we get that 8% in this pack Travis Sanheim. Oh My goodness.  All right, sure Artem Zube Shane Gossas Bear All right an icon not an icon. We want to pull those a dino chara Brady Shea Okay Come on something good here, baby. They're saving all the 80 pluses till the end here is what it's looking like I don't think we pulled many 80 pluses here. No, okay. We pulled a couple. We pulled a couple There's still a couple left though. That's a good thing.  It's fine. We got one more pack left here This is the last pack and we're hoping for something good here. Come on EA. Show me the money Peter Mirazek, okay guy who's always getting injured play two games of the leaf injured twice love to see it Anything else in this pack here? Ryan Murray is not ideal Nick Patan former leaf Calvin Picard former leaf Chernak. Oh my goodness. Are we not gonna pull anything in this pack as well?  Don't give out. We got 150 left It's enough for a premium pack. We're gonna skip it and hope for the best here. Come on. Yeah Connor Brown and that is it and why not for shits and giggles. I don't need any of these cards for collections We're gonna do one more 83 to 87 overall And we're gonna hope for something. I don't know what I would want from this But like anything 83 or higher Obviously is gonna help out for some of these master sets. So here we go last pack of the video. Please be something good It's an 84 Quinn Hughes. It's an 84. We'll take it. We will definitely take it Okay, Quinn Hughes. Thank you. Anyways guys, that's gonna be it for today's pack opening video I know we didn't pull much Petrangelo Quinn Hughes. That's about it, but we tested our luck Let me know if you guys think this is a this new event is a W or an L. Let me know. That was a horrible ww Or an L. Let me know in the comment section below But guys that is it for today's video if you guys did enjoy be sure to drop a like on it If you guys are new around here, make sure to hit the subscribe button down be low Well, like I said guys that is it for today's video. Thank you guys very much for watching and I'll talk to you guys later


Everybody forced here up in 2021 flawless football hobby 1 box number 53 left side serial numbers That I drop a Lincoln chat Let me get a Lincoln chat. I'll show you the results right after I'm also gonna call out whose hit is who's as we go along here There's a link here are the results on screen for you for a moment. Good luck everybody. Let's see what we got Any of the number 26 goes the illegal deal. All right, we're gonna start off with a Super Bowl patch card Marcus Allen numbered 19 of 25 19 spot is Robert s Yeah, Kimberly you can have 27 That's fine Jumbo patch Aaron Rodgers one of 25 one spot Jesse a TJ Hushman Zotta auto that is numbered 19 of 25 19 spot again Robert s Laundry tag Auto Matt Ryan three of three Sick hit boom Ray J with the three spots Nice Matt Ryan got a shield swoosh all in that laundry tag Excuse me guys my voice is still a Bit a bit damaged from the national All pro Inc John Randall numbered to a 15 Two-spot hit for Sheldon J John Randall Nice one here patch auto Jalen Hertz 12 of 15 Nice Jalen Ray J with the 12 spots as well Good break for your ray We'll mag the Hertz the four colors on it.


What's up everyone it's your girl Kenzie here from Layton Sports Cards and I'm ripping a brand-new release today at 21 22 Penini Donneress Optic basketball hobby six spots break number seven pick your team I'm gonna go over the teams and then we'll get started. We've got both hobby Clippers Christopher M Hornets Dylan s heat Evan M kings Francisco a wizards Jeffrey H with the calves and warriors Joe R. Hawks Jordan and Blazers Jarell E grizzlies Kyle M with the magic and T wolves Larisac Y Spurs Long J Nuggets Matt S Bucks Michael C Nets Moe S Pelicans Patrick C Sons Peter R Bolz You've got Sacko K Piston Sacko K also with the Raptors Scott Y Thunder Shane M Mavs and Sixers Sorvige and T with the Jazz Steven C Lakers Steven Roy S Pacers Von B with the Celtics Wayne S nicks and Yip H with the Rockets Alrighty best of luck everybody. Here we go Get no photon in the last case. This is our last case of the day Let's see if we maybe get to 75 years Jamal Murray all stars gonna roll the dice here one two three left four five six that'll uh be One two one two three left four five six right that will go for the rest of the break unless it is a one of one. Good luck There's a three so that will go left left ad the pelicans. So all the all-star inserts will go to the left Got Moses moody rated rookie. Let's see style old hollow star G's and Katie Jalen sucks rated rookie hollow Darius Garland Barton McBride reading threes Duncan Robinson Hollow Michael Porter jr. The rookie Isaiah livers pistons They run sharp. We've got hollow elite dominators Nicola Yolkic No one-on-ones yet card palace. No no gold vinyls yet. We do have a gold right here though Jason Preston We do have a gold right here back-to-back breaks with some gold We have jimmy buckets for the heat five out of ten Miami That is Dylan s. There you go jimmy butler gold Nice hit there Davion Mitchell that only has three cards in that Five I believe got evan mobly rated rookie Lukadanshich pink velocity of Jonas Valenkunis for the pelicans 66 of 79 Raider rookie Jared butler kade cunningham on the 75 years We've got sons out of 99 dominators auto elford payton Suns Otto there star gazing Zion williamson Bones highland rated rookie. We've got hollow ja marant. What's up tiktok? Hope everyone's having a great friday brain embossed junior. Thanks for tuning in support the stream. We've got lime green out of 149 nuggets michael porter jr Shenkun we've got red star gazing donovan michael 36 out of 99 nice one there Heck yeah Luca garza hollow raider rookie j.t. Thor Jalen green we've got orange dairies basely to 199 53 and 199 thunder Gensik talk we'd like to hop in some breaks later tonight with porous Link is in the bio Kessler edwards chris middleton lighted up box two box two here And let's see a big rookie photon all the photons we've pulled have been uh vets so far today I'd say it's on hollow carousel overt Oracle vinyl that'll be pretty sick too. I haven't seen any of those yet either chi jones lebron star gazing Uh 35 years lebron james I'd say it livers the rookies red insert 10 of 99 Jalen green for the rocket. It's nice when they're houston on the color match Who's got houston this time around yip h? Here you go yip on the red Jalen green the rookies will mag that for you G2 Thor who's my garuba hollow chris duarte raider rookie I'm gonna go left jason tatum tree man raider rookie light it up tray young Hello, isaac stewart draws bassey. We've got orange to 199 germy grant pistons charith cooper 75 years dwayne wade We've got out of 99 retro series of tom satch sanders for the celtics celtics throwback hit there last Janus elite dominators Very rookie Cameron thomas. We've got ad. Uh, hollow train springer Zion red 4 of 99 pelicans Gentics off link in bio if you'd like to check out the website Got these available for personals more group breaks over the weekends And more group breaks later tonight with force with spots still remain leighton sports cards dot com hollow the rookies kate cunningham You go pistons. Nice hollow kate Got scotty barns raider rookie derrick rose light it up kairi All right, erin wiggins. We've got lime green 117 149 josh giddy thunder boom There you go thunder. Wow scott wide clean giddy thereto beautiful hits We'll mag that one for you heck, yeah Very nice We've got 75 years moses moody I'd say a jackson lime green to 149 Kyle Lowry shorter gonna go left to white Howard. All right box three Box three low anthony edwards hollow clay thompson low from germany. What's up bob? Franz Wagner raided rookie james wiseman stargazing chris paul wise camp ant man josh chrisfer the rookie scottie barns insert 35 years moses moody the ayado sumu norman pal light it up russell westbrook Grimes hollow raided rookie germaya robinson earl thunder kate cunningham on the rookie base blue 59 buddy healed for the king's 24 59 three city bang erin wiggins. We've got orange jared butler out of 199 jazz 90s one there jazz jared butler No, believe it or not math town women do enjoy sports as well We don't only belong in the kitchen, but thanks for your comment The cozy mac jones rookie card scottie barns raided rookie derrick rose and chris middleton Here we go Yeah, optics always a fun fun Rip optic of zubat for the clippers Blank in bio if you'd like to hop in any breaks later tonight We've got all stars hollow of yokich for the nuggets Up cosmic no going to the kings. We've got raided rookie on card davion michael We go kings all stars trials barkley on the left Doing good bull. How are you doing? Like a four two or three day weekend. We've got hollow lamella ball Look night. We've got lime green denise schroeder. I love the lime greens with the saltics card just pops 81 of 149 75 years sga Yes, this is a group break Already um filled up jonathan kominga and hollow lighted up steve curry. This was a pick your team format Six spots half case break box number four Oh, man Unbelievable Same here. Appreciate you hanging out with us though Um, like I said, k g these are already paid for spots We've got out of 49 train man on the optographs for the thunder nice one there train man Dominators, uh jimmy bucket hollow raided rookie darin sharp got red carl anthony townson 99 tea wolves Jean springer. Zach Levine lighted up Yeah, johnson. We've got kairi Irving all our all stars hollow left side Nope, you can buy uh buy spots on a break if you'd like some cards. We've got lime green to 149 cherry rosier hornets link in the bio 75 years chris middleton There's my garuba star gazing lebron kory kisbert hollow clay thompson Got hollow star gazing yokich All stars gonna go to the left to white howard Here comes the thunder about to say chris duarte raided rookie clay thompson about that time of the day train man raided rookie and hollow andre drummond sixers um retail usually releases a couple weeks after gills I don't think optic retail released the same day out of 199 rj barrett nicks Like I said, it's usually a few weeks behind Got 75 years. Clyde draxler. I don't even think select football has come out yet retail We've got optic brandon ingram. At least I haven't seen any time bringing threes rey allen chi jones james harden 75 years Got red all stars going on the left side kairi for the calves. That is 76 of 99 pack box four Hollow divante gram pelicans. All right box five Okay, everyone all filled up for the daytime. I've got one more half case break after this And then that'll do it for the daytime and of course we'll start back up at five with some soccer Let's get that bonus league of tier one 12 box case break random team filled up for them sga. Hollow. Gotcha Bones highland raided rookie star gazing step curry Yeah, I would I would probably give it a few week skills and look look in store then hollow mcow bridges What's up tiktok? Hope everyone's having a great day Lincoln bio if you'd like to check out our website Got bluetooth 59 Spencer din witty wizards 25 of 59 moses moody raided rookie raining threes trey young Luka garza hollow. Jeremiah roms and url thunder Jalen green raided rookie lighted up trey young me honest dominators Tessler edwards julius randall Come on. Let's see some big big auto come out of here. I'm still looking for photon too Raided rookies are williams hollow tj warren 49 pelicans optographs rookie of trey murphy the third Pelicans All stars on the left jason tatum Jalen sucks raided rookie and hollow jordan clarkson Miles McBride dameron sharp on the ping velocity is 79 for the net That is 71 of 79 nets 75 years alonzo morning shingoon elite dominators donovan michael hollow Aaron sharp. We've got orange the 199 city bay pistons Doing good ellie. How about yourself? Preston desmond vane Maybe i'm michael briley biel We're looking for more giveaways the late gaming channel does a lot of giveaways especially on the tiktok community So definitely check check us out on on that platform dream on green hollow late gaming official twitch youtube tiktok Caleb does lots of giveaways Got evan mobly raided rookie luka donchich and elite dominators joellen b nice elliot On some optic boxes Last box here this box of the brakes still looking for photon It might be in the second half of this case. We didn't get one of the last case Quentin grimes going to go left ad got kade cunningham raided rookie in 75 years john stockton keto we've got blue elite dominators for the lakers ad that is 20 28 of 49 hello raided rookie david johnson so brooklyn Got scotty barns raided rookie and to 99 for the bulls optographs of iodo sumu Seeing lots of him today. There you go bulls jason tatum elite dominators Jackson going to go left sef curry That mirror lights just flickered Okay, josh kitty raided rookie john wall james hartin That's scotty lewis hollow cameron johnson Here we again to got red the 99 miles bridges for the hornets 36 of 99 We got 75 years lebron james. Yes. This is a hobby box hollow raided rookie xyre williams Yes brainer released today optic basketball 2021 22 Herbert jones hollow star gazing james hartin light it up kairi erving J.T. Thor we've got orange to 199 derrius garland calves They've got 75 years dewayne wade for the heat hollow john collins hawks Got lime green cristo arte pacers out of 149 56 out of 149 another nice hit there pacers sentiel dama zion williams and star gazing iodo sumu for the uh raided rookie and reading three tollow damian lilor And hollow sef curry sixers All right, let's do a recap real quick. Here we go Got the kade cunningham hollow for the pistons gold jimmy butler 5 of 10 our autos the tom satch sanders Celtics a elford payton's sons dating on michael king's iodo sumu for the bowls That was 26 of 99 a tray man rookie autos 17 of 49 and tray murphy the third 40 of 49 Our magged cards. We had the green josh giddy for the thunder 117 of 149 And then the red the rookies jaylon green That was 10 out of 99. All right, everyone that'll do for that break. We've got one more of these coming up next. Thank you