Hello, welcome to NPTEL NOC, an introductory course on Point Setupology Part 2. Today we shall continue with our study of the separation of sets, module 39. So, we have seen a number of implications and some non-implications also, but now under compact half-top space we will see that all the four axioms are equivalent. So, this is the statement, if x is a compact half-top space, then S0, S1, S2, S3 are all equivalent to each other. As I told you, we have already proved under T1 as S3 implies, S2 implies, S1 implies, S0, right, just because every point is closed, that is all we have to use. We have also proved that under Lindelofnes, S2 implies S3, the reverse implication. So, it remains to prove that under compact half-topness, S1 implies S2 and S0 implies S1, okay. So, before proceeding further, I will state a lemma which can be used again and again and of course it will be used in proving these two statements. So, the lemma is take a compact subset of a topological space x, okay, take a point P in the complement of F. Remember, F is a compact subset, okay, so I am taking the point outside that one. Suppose every point of F can be separated from P inside F, then there exists a clopon subset W of x such that it contains F and does not contain the point W. So, from point separation here for each point, for each point of F can be separated from E. So, what I have done is, I have taken the hypothesis of S2, but only for points of this compact subset. So, that is slightly generalization than assuming x itself is compact, that is all. But that will be useful for us. So, what we do? To each point Q inside F, we get a separation, that is the hypothesis. x equal to AQ per BQ, P inside AQ, Q inside BQ. Remember, this just means that AQ and BQ are both open and closed and they are disjointed. Since F is compact, F will be contained inside BQs because Q varies over F. Take the union of all BQs. So, F is inside that. Now, each BQ is clopon, in particular open. So, we get a finite cover. So, I can write that I range from 1 to n BQI union containing F. So, this I am denoting by W. So, that is my choice of this W, which is obviously open as well as closed. So, being a finite union of clopon, that is to open, it is clopon. Clearly, P is not a point of any of these BQs. So, P is not inside W also. So, over. So, compactness has helped us here. Just like in the case of Lindelof, we have got S2 implies S2. Now, we will use this lemma to prove both these S1 implies S2 as well as S0 implies S1. The first one comes very easily down. Let X be a compact half-door space satisfying S1. Let F be a closed subset of X here and P belong to X minus F.  So, we can apply the previous lemma to this closed subset F. So, what we get? We get a clopon subset W such that F is contained inside W and P is not in W. So, this is just a almost restatement. Instead of X compactness in the lemma is assumed, F itself is compact. So, because F is closed, I am getting the hypothesis. Now, let us try to prove S0 implies S1. This will take a little more time. So, S0 implies S1 means what? S0 means what? Singleton are all components. From that, I have to prove that distinct points can be separated. So, let X satisfies S0. Fix a point P inside X, look at all the points Mp, all the points Q, this Mp is all the points Q which cannot be separated from P. What we want to prove? We want to prove that every point other than P can be separated. Therefore, what we have finally proved that this Mp is only singleton P. So, there are steps to prove that. So, how do we are going that? First of all, P itself is in Mp. So, it is enough to prove that Mp is connected because the only connected subsets of S0 are singletons. If there are more than two points in any set, it is disconnected. That is what S0 means. So, what I will prove Mp is connected. So, it is singleton and then the proof is over. So, let us try to prove that Mp is connected. The first step is to prove Mp is closed. This is the strength thing. So, why do we need to prove that something is closed if it is a connected set. So, let Q be a complement of Mp. Q is in a complement of Mp. By the very definition, what does this mean? All the points here are points which cannot be separated. It is simple as that there is a separation. X equal to A bar B, P inside A, Q inside B. That is the meaning of a point is not in Mp. But then every point inside B, remember this means just B is an open subset and contains Q. Every point inside B is also separated from P by the very definition. It just means that B is contained as a Mp closure, Mp complement. So, for each point inside Mp complement, we have formed an open subset contained inside that one. That means this is an open subset by itself. It just means that it is a complement which is Mp is a closed subset. So, we have proved that Mp is closed. Now we can complete the proof that Mp is connected. Suppose this is not connected, then we will arrive at a contradiction. Not being connected means there is a separation of Mp itself. It is not separation in the whole space. It is separation of Mp because it is not connected means there are two points which cannot be separated. So, it is a non-empty separation if that is all. So, I can assume P is either inside C or inside D. So, let us assume P is inside C by changing the notation if you like. We shall show that points of D are separated from P in X itself. See, this is separation inside the subspace Mp. In general, it does not imply that these two points can be separated in X itself. So, that is what we want to prove that. That is the hardest part here itself. So, we want to prove that. Once we prove that, there is a contradiction because these points of Mpr what they are points which cannot be separated. So, now we are proving that there is a point here which can be separated. That is the contradiction. So, how do we do that? C and D are closed subsets of Mpr. So, they are closed in X also. Here where we have used that Mp is closed. The passage from the subset to the larger subset. So, you have got disjoint closed subsets inside X. Now we use X is compact after therefore it is normal. So, therefore there exist open subsets U and V. C contained in U, D contained in V, U intersection V is empty. Disjoint open subsets. That is normality.  So, U bar intersection D will be empty. Since C is inside U, it follows that boundary of U intersection C is empty.  So, boundary of U intersection C is empty because C is inside U. Therefore boundary of U intersection Mp which is Mp is C union D. So, take boundary of U intersection C and boundary of U intersection D both of them are empty, union is empty. So, this means that for every point of this, let me call it as F, this boundary of U, these points are separated from P because it does not intersect this way. So, they are not inside Mp. Boundary of U intersection Mp is empty. What is empty? Everything in Mp cannot be separated. So, these points are separated from P. Boundary of U is what? It is a compact subset because it is a closed subset of a compact subset. So, now again I am using this lemma with which we started. It follows that it is a closed subset W such that this F is contained inside W and P is not in W. F is boundary of U. So, let me repeat what the kind of things we have done here. So, here is a picture. We started with the separation C here, the square, another square here D. So, this is a separation of Mp. After that, using the normality, we found out U and V which are disjoint open subsets containing C and D respectively. Then look at the boundary of U. So, that is this F that does not intersect C nor D. That is what we proved. Now, using the lemma, I can pattern this F to an open subset W. So, this shaded part that is W such that W is a neighborhood of F and it does not contain this P. So, this much we have done. So, that is what the F is contained inside W and P is not in W. So, how does this help? Now, you can complete the proof as follows. Look at G which is U minus W. So, this is U here and U minus W. You have to throw away all the shaded part. So, what you get is this G unshaded part. Clearly, that contains this entire of C.   So, G intersection is also empty. Since U is open and W is closed. So, G is also open. On the other hand, boundary of U which is F is contained inside W. So, we have G equal to U minus W. This is by definition same thing as U bar minus W because the boundary is taken care here. Boundary points are all contained inside W. I am subtracting that part. So, G is U minus W itself. You can write that U bar minus W bar and just a real expression. This used now, this is closed and this is open. Therefore, this G is also closed. So, we have found a cloak on subset. It shows that points of D are separated from T. We have got a cloak on subset containing P and D is outside. But D is inside MP. We started with a non-trivial separation. That is the contradiction. So, what we have now? Compact plus half star. All the four axioms are equivalent. So, that is one of the reasons why we studied them. However, life is not that easy. We want to study them slightly larger things. Non-compact things are very much needed. So, that is why all these differences have to come there. Most probably, we can assume Hausdorfs' actually finally in the dimension theory that we are going to develop, we are putting matrix base also no problem. So, but we do not want to put compactness. So, that is why all these. So, we will continue to study of these things a little bit now which will be useful later on in dimension theory. Take a T4 space which is written as countable union of closed sets. Each of them is satisfying S3. Then X also satisfies S3. So, let us prove this one. K and L be two disjoint closed sets inside X. K equal to G0. L equal to H0. I am starting a process here, inductive process. Inductively, we shall construct sequences of open sets GI and HI of X. GI minus 1 bar is inside GI. HI minus 1 bar is inside HI. Each CI is contained in the union of GI and HI. GI bar intersection HI bar is empty. For each I will do that. The starting thing is K equal to G0 and L equal to H0. What are K and L? They have been given to be disjoint closed sets. So, there you do not have to verify. You have to verify only the last area. So, we can then take, once we have such a sequence, we can then take G equal to union of HI. H equal to union of HI. This G will contain all the CI. This H will contain all the HI. Therefore, G union H will contain the whole of X. So, starting with K which is G0, that is also contained inside G because G is union of all the GI. Similarly, at least L is contained inside X. Finally, I want also to show that G bar intersecting H bar is empty. Once we have this one, we have this sequence, we would have proved something. So, apply S3 to G0 intersection G1 and H0 intersection C1. This we do now, both of them are subsets of C1. C1 satisfies what? S3. All CI is satisfying S3. So, I get a separation A1 union B1 equal to C1, separation of C1. A1 intersection B1 is empty and A1 will contain the first set and B1 will contain the second set H0 intersection C1. So, successively we are applying S3, S1, S2. So, now observe that A1 and B1 are closed inside X as well as closed inside X also because why? It started with A1 B1 closed inside C1. C1 is closed. So, that is also hypothesis here. Each CI is closed inside that X, union of countably many closed subset. So, they are closed subset and G0 union A1, H0 union B1 are disjoint closed subset. G0, H0 were closed anyway. Therefore, I can apply normality T4 as I have assumed for X. Now, I can pattern these things. There exist disjoint open subset G1, H1 such that this G0 union A1 is contained inside G1. H0 union B1 is contained inside H1. G1 bar intersection H1 bar is empty. Obviously, C1 which is contained inside A1 union B1 is contained inside G1 union H1. So, the construction of this sequence for i equal to 1 is over. From i equal to 0 to i equal to 1 we have done. You repeat this step with now you know depressed not by 1. The same thing you repeat for next one. You will get A2 B2 G2 H2 and so on. So, from i minus 1 to i plus 1 you can go. So, that we have G i bar intersection C i plus 1, H i bar intersection C i plus 1 inside C i plus 1. You apply the same thing to get G i plus 1 and H i plus 1. So, once you have done this you get this statement and that completes the proof. I would like to sum up a number of implications and non-implications which we have proved. Just this could be like a ready made reference you know ready recon for you. So, this is the picture. In this picture the solid arrows like this like this they indicate implies S1 implies S0 like that which is always true. So, I have put a solid arrow. A broken arrow by N here this arrow is not solid arrow broken and put N. N to indicate does not imply S0 does not imply S1. What is the example our Koratowski, Kraster Koratowski example is minus the apex point is K0. So, I have put it in a bracket to remind you what gives you this example. So, like this we have under T1. So, I have indicated with T1 S2 implies S1 under again T1 S3 implies S2 right under compact and half door just now we proved S0 implies S3. In fact all of them are equivalent anyway. Once you have got here you can come back like this. So, all of them are equivalent. So, I have shown one arrow that is enough then you can keep going. But we have also elementary example that if you take S3 may not imply S0 in general. What is the general space? The Sierpinski space remember Sierpinski space consisting of just two points. One point is closed other point is not a closed set. One point is open other point is not an open set. There are no disjoint closed sets. No disjoint non-empty closed sets to be present. Therefore S3 is automatically satisfied. But at different point you cannot separate them. It is connected space. So, disimplication is not true. And also you have proved that under Lindelofness S2 implies S3. If you have more things you can accommodate you are welcome but I think this is enough. So, by the way this set of all points is all coordinate rational inside the L2 space little L2 space. So, that came in an example of an S1 which is not S2. So, this also we have proved. You can go and see where they are there. So, this is roughly a thing that may be many other example many other things like I do not know in general whether S3 you know without T1 can you have S3 imply does not imply S2. Without Lindelof example of these all those things we have not discussed. So, lack of time also lack of interest also. That does not mean that we have completed the whole thing. So, that is not the whole idea. This is just an introductory course not meant to be comprehensive. So, next time we will start the theory of you know topological dimension theory is genuine. So, all these were more or less like a background preparation. Thank you.


Hi, everyone. This is Victoria English, top coach with Project 90. I am taking over James's podcast yet again. And I have the honor of interviewing a wonderful member of our community, someone that I just adore. She brings so much to our group, such a great personality, and has so much to share after recently completing 90 days with Project 90. She has been alcohol-free for about 95, 96 days, something like that. So she is just crushing life. And she has done the honor of interviewing with me today. Melissa Higgins is from Pennsylvania. She lives in a small rural area about an hour outside of Philadelphia. She's married to John. She has five children. She works in a commission job. And when she came to Project 90, she stated that she had a lot of stress in her life, a lot of anxiety, so much so that she would wake up in the middle of the night feeling it. She is in her 50s. And like many of us who are at that age, she wants to enjoy life and recognize that alcohol was taken away from that, from her quality of life, from her ability to enjoy things. So she joined us. And through this journey, has shared that she has gotten to know herself better, has learned a lot about herself. And she told us that people would often tell her that, Melissa, you are one of the most optimistic people we have ever known. So we'll ask her more about that. So please join me in welcoming Melissa Higgins. Hi, Melissa. Hey, Victoria. It's day 98. I'm so close to the 100. Whoa. Yeah. 98 days. Before we dig into your story, how do you feel today? 98 days alcohol-free. I feel fantastic. I feel great. I feel excited about the future. I feel like, why did I wait so long? I physically and mentally feel better in everyone. Yes. And I've had the joy of watching Melissa and coaching her through this journey. And the physical change that occurs, and I know you see this in our other members, Melissa, but the physical changes that occur at even 30 days and then getting to 90 and now beyond 90, it's just incredible.  Your skin's clearer.  Your hair shinier.  It's amazing. Do you see that change in yourself? I do.  I do. I think I'm less puffy and physically. I mean, that waking up in the middle of the night, I still have a very stressful position at work, but I do not wake up in the middle of the night at all. Most nights. And maybe it's just to use the bathroom. Yes. But I was waking up and I couldn't get back to sleep. And now my sleep pattern is better. I have lost weight, although I haven't, and I haven't even dieted. I have always been a healthy eater, so I'm eating healthfully and I'm thinking tackling one thing at a time. I didn't put too much on myself mentally. I always try to eat healthy, but I thought I'm not gonna push the weight loss. And I have, it just comes off when you're not drinking but and drinking so much more water and good things. But yeah, I thought I'm gonna do it slow, lose weight slowly, healthfully, keep it off. Nothing like gung-ho, you know what I mean? I wanted to just kind of ride it out and do all the right things and take my time with it. For sure. And that's something that you've probably heard us talk about on our group coaching calls. Oftentimes people come in and they start to feel great when they give up the alcohol and then they decide, you know, I think I'll give up dairy and gluten and I think I'll start training for a 10K. And I think I'm gonna start that memoir I've always wanted to write. And that's wonderful. And that's what the Beyond 90 is about, but you had the right attitude in just taking one thing at a time because giving up alcohol is a big deal. Yeah. A lot of layers. So just let the feelings come, let the process happen, don't stress about one thing, don't stress about another thing, just kind of let it unfold. And I just can't believe how fast it went too. It's just crazy. I know. It's been such a great experience. Thank you. Thank you. Yep. Well, it's great to have, I mean, all of our members, we have such a great community and so much so that Melissa is even organizing a get-together in New York City with some of our members. So that's just an example of how close we get in this community. We're literally from certainly different states, but different continents. And that's how connected we all become. It's a really special, special experience. You know what? It really is. Why could jump in? I am just astounded at what a loving, connected community. And I've met so many people and we really do wanna stay in contact in that trip that you're talking about. I mean, people wanting to come from California, Arizona, Ireland willing to jump on a plane and so we can all meet in person. And I just found that to be so, you know the word, like heart and heart, it's more than heartwarming. It's just like, wow. It's as well. It's mind-blowing.  You know, we have members where their doctors are saying, okay, you gotta take a break. But it is amazing when you come in and you realize it is so much more and we'll get into that as well. It is so much more. And you're right.  Almost, it's like, great. It's my cholesterol is better than it had been for the past three times. And like I said, nothing was ever alarming. I never had a doctor telling me you have to do change your lifestyle, but the proof is in the results. So there you go. For sure. And you and I are both in our fifties. And so we can attest to how things don't come so easily anymore. You know, it's, you don't just go in and take it for granted that you'll have perfect blood work. You oftentimes, I mean, with the hormonal changes that we go through the weight gain, even if it's not substantial where you're like, oh my gosh, I don't fit in anything in my closet. It's so much harder for the weight to come off and our metabolism naturally slows down. And yeah, when you remove the alcohol, it just, it does give you quite an advantage. Yeah, yeah, it is amazing. I have a pretty serious back issue as well. I used to be a real exercise advocate and exercise constantly and at the gym every day. And I came down with, I don't know, I guess, spondyl lysis. I don't even know how to say it. Final sciosis. I have, I have a fusion, one fusion and now I have a fracture below it. I need another one. So it's really hampered my ability to exercise. But so I need to try to get back to at least doing the PT for my lower back and strengthen up my core. But hey, being alcohol-free, that was one of the things I think that really got me, my daughter's in the fitness and nutrition industry and she just felt that the inflammation from the alcohol, no matter how much, it wasn't a lot of alcohol or she felt that it would be to my advantage to not drink. For sure. Yeah, alcohol, if our listeners don't know it, alcohol is one of the absolute most inflammatory things that you can put into your body. So any of those normal, you had an exceptional issue with your back, but just the normal things that happen as we age, as you know, I'm a Pilates teacher, a nutritionist, I've always been very fit, but still you wake up in the morning, you're just a little more stiff and things are not quite as loose as they used to be. And yeah, the alcohol just makes it so much worse. It is, it's harder to take the weight off now and that did not help. It didn't, I know. So let's just learn more about you, Melissa. Talk to me a little bit about where you grew up and what your childhood was like. Oh gosh, I'm the youngest of six children. I grew up in the area. I've not strayed far from home or my siblings. Had a wonderful childhood with loving parents and non-drinkers. I mean, they were people, my mother, I think never, she was raising six children. My father worked very hard and did well. And yeah, I had a fantastic childhood. My siblings, you all get along. We're all fairly close. I have one brother that lives further out in Washington state on the other side of the country. But yeah, it was a great childhood. And like I said, I had parents that were not drinkers. My father occasionally, but so, I mean, that didn't affect me at all. Yeah, I always like to learn about people's backgrounds because often it's assumed that if alcohol becomes an issue in someone's life that, oh gosh, they must have grown up around it or maybe their parents too much. That's not always the case. I think, and we'll get into, of course, you and I have strong feelings about society and the way women are targeted with alcohol. We all are, but I take a special issue with the way women are targeted. So that's why I like to learn about people's backgrounds. So you were not exposed to heavy drinking or anything like that. No, not at all. It wasn't until probably, even I had kids early. I got married very young-ish and had kids early. So I wasn't even really drinking during that time. I would have wine, but of course, I don't want to add a baby every other year. So it was the nine months of not, and then I would have red wine was kind of my drink then. I think it wasn't until in my 30s really when we moved to our current neighborhood when the kids were right before they started kindergarten. And it was a really social neighborhood. I mean, neighborhood parties every day, like, other week. I mean, like I said, everyone has to fit a few acres of land and we'd have bonfires and they'd be on four-wheelers and the parents would all be around drinking. Yes. Probably while it was dangerous, while the kids were playing bonfires and setting off fireworks and- Ah! I want to go bonfire. They probably were really crazy. But you know, it was a good time and everyone had a great time. And so I think that's probably when really I probably started drinking on a daily basis. So what I hear you saying is that it was never an issue. You were pregnant every other year. I was the same way. I had my first three and four years. Was it two and three or four years too? Yeah, so alcohol was certainly not part of my life and then of course the nursing and the sleepless nights, there's no space for drinking in that time. But it sounds like we differ a little bit because as I've shared in my story, I was a quote normal drinker until my mom died suddenly. I was left with a lot of trauma and began self-medicating with alcohol. So mine wasn't so social. So that's an interesting thing. So it sounds like you were just with all the parents having neighborhood parties and then were you surprised to find yourself drinking as much as you were? Not at that time.  My mom died and then my dad just kind of gave up. And that was really sad because I felt like maybe like we weren't enough for him to want to keep on going but they were married, gosh, almost 60 years and she was just a love of his life and he just didn't want to be here without her. So that was very sad and depressing. My back issues didn't help. So but yeah, I think it started out as a social thing. And then it's like the stress from work, you come home, I have a stressful job and it is commission. I'm in new construction, real estate. So it's a little bit of high pressure. So I think it started to become just that what's my reason that I wanna drink today? I'd make it out of my head, maybe on the way home in the morning I'd say, well, I'm not gonna drink tonight. I don't wanna drink. But then it would become like I'd come home, first thing I do, kiss at the counter. I'm not even changed yet because that's why I come home, I get changed. I take off my work clothes and put on like, if you saw me after as the air goes to a ponytail, I'm in with my pants, I'm in the sweatshirt. It's a complete transformation. I would have that, I'd have to have that drink before I even did that. The kiss at the counter for myself a glass of wine or whatever I did, drinks with a stronger alcohol as well like vodka or tequila. But I'd have to have that first like couple sips and then get changed. And I would also like to, I like to cook. So it was kind of my ritual of having a glass of wine or something while I was cooking. And my husband, maybe you would have it and he's my husband's not a drinker. So that really helped. But he'd have something and then we'd have to have a glass of wine with dinner. So it was kind of like continuing from coming over from work and the whole cooking ritual. And it seemed like looking back, I was looking for as much as, so I'm probably jumping ahead to when this all started to why I felt like I wanted to stop this. Yeah. Yeah. I want to touch on something before you get to that part because what you said was interesting. And I want our listeners to understand something. Very often, naturally when we're socializing and because of society, everyone drinks. It's just what you do. It's important to understand that even when we are drinking socially and having fun and maybe not really suffering any consequences other than a little hangover the next day and kind of laugh it off and all the parents are kind of joking about, oh, we had a little too much last night. Let's go a layer deeper because what's happening there is you are setting up neural pathways in your brain that expect that addictive substance. When something stressful happens and it sounds like obviously the loss of both of your parents within, it sounds like a pretty short time. Say about a year and a half. Oh gosh. Okay. So Melissa lost both of her parents to whom she was very close, a close knit family. If you listened to what she just said she went from the social part of having fun with the neighborhood and that's great and fun. But then you hear it shift a little. Maybe she was still drinking with the social gatherings and everything but you hear that shift in the meaning she attached to wine. It sounds to me and correct me if I'm wrong. It sounds like it went from being something that was just really fun to something that you attach to the end of the day stress release, time to relax, time to numb out a little bit. Yeah, exactly. And now all that. Yep, yep. So that's an important thing as if you're listening to understand about how insidious this can be. So for me it was definitely more of just a big moment because I lost my mother. I was having, it was 1999. So we didn't know what we know now about anxiety and panic attacks but I had been a runner all of a sudden I couldn't run. I couldn't catch my breath. I was having anxiety. I needed to see a doctor but I didn't know. And that's where my drinking took a hard left. Melissa, if you are listening closely it was a little more insidious but the meaning that you attached to it changed. So I think that's really interesting and really helpful for our listeners to kind of look back on their experience with alcohol and go, huh. Yeah, I can identify when it changed a little bit. Yeah, you saw that. I didn't think about it until you said it that maybe it started out as fun and then layers of life, like things happen and then it could change into something. Right, right. Well, it's like I'm a coach or something. Really? I know, how did you, yeah, it's amazing. I think I spent a lot of time thinking about alcohol. Well, but in a good way now, not like I used to. I used to spend a lot of time thinking about alcohol and when I could get it again. But anyway. Tonight. Yeah, that's very telling. That's very telling. So, okay, so then you move into, all right, I'm working so much, I've lost my parents. I need wine to relax. Wine signifies relaxation just like my sweatpants and a ponytail at the end of the day. That's true. And I didn't work when my kids were young. So that was different, you're right. It kind of compiled into then I started working full-time when they were older with a stressful position and yeah, I'd come home, like I said, hit the keys at the counter and would have a drink and I feel that it went on for a time. And then I started with every morning thinking, well, this will be the day. I really think that I need to stop. And at some point during the day, my mind would shift and I find that reason whether you create it with, I still have the same stress that work. I still have the same things happening, but you have to make that decision. You just have to make the decision.  It's just project 90. I'll tell the listeners made it so easy. And I know that sounds crazy because if you're out there and you're thinking I do the same thing every day and I wanna do it today, I'm gonna think I can't. It was like magic. I think a lot of it is the community. Yes. The coaching, the interval coaching, the calls, but they probably don't know there's a market full of community where everyone can post a video and talk to each other. And I'll tell you, I looked forward to my ride into work and my ride home. I just couldn't wait until I could put the turn that on and hear everyone and then respond, reply or do my own. It really, and I was reluctant in the beginning, I have to say, I was a little reluctant, don't like to be on video, but I do it a lot for work now. We have to do a lot with videos in Zoom calls and team calls and bomb, bomb videos and talking to people through video because people really feel that connection. So it became easier and easier. And I'll tell you, I just love it and look forward to it. And it has made it, I'll tell everyone out there, super easy. When you were, when you talk about before Project 90 and you said, okay, today is the day. Did you, did you attempt moderation or did you say, you know what, this is just too much, I'm stopping? I think, yeah, I attempted moderation and achieved that at times. And, you know, we'd maybe go 30 days or maybe even try to maybe just have a drink on the weekends, but, you know, it just always seemed to creep back in to maybe then it would be, okay, I'll have a just drink all the weekends, but maybe then Monday night was really stressful and I had meetings all day. And now I'm gonna get a glass of wine. So then one turns into two and two turns into three. Yes. And then we're opening a while of wine a night and sharing it, you know. Right, right. And I think that's so common. We all have gone through that where we say, okay, you know, I'm just gonna have one or I'm going to have it on Friday, but, you know, Wednesday's really tough. So I'm just, I deserve it. Right, right. Yeah, yeah, let's talk a little bit. And I love what you're saying about the Project 90 community. And you've been, again, like I said, such a big part of it. And that is a key to success is getting involved in being vulnerable with the group and sharing and taking an interest in others. When you, I lost my train of thought. I had something I was gonna say. No, that's taking an interest in others. I think that is so important. And it's because I think I remember my first Zoom call. I hate to even admit this. I was like, oh, I don't know if this is for me. I don't wanna hear, I can't listen to more problems because it makes me depressed. And then, you know, maybe I'll direct it. I'm so embarrassed to say that, but it feels so differently. And I think from that time on with the next one, you just have to really listen to people. And I think it is a big part of it and get taking an interest in other people, what they're going through and what brought them to this point in their lives and how you can contribute. And this is, even with the Mark of Holes, just amazing how you're not even talking face to face. You're doing videos, but it's just the secret sauce of it all, as we say. And then Zoom calls it, just hearing people and listening to them, and everyone's so positive. And that's the other thing. It's not, no one's branding you because many of us, you're not really an alcoholic. You just don't wanna drink as much. And you can see that it's affecting your life. It's affecting how you wake up. And I never really had a hangover. I always was someone who, you know, if I say I'm gonna do something I show up, I push through, get up one time, I'm at 100%, but, you know, and now I feel like maybe you're not really 100%, but you thought you were 100% because now you're clearer, you're more clarity, you wake up with energy and, you know, can, you know, have more ideas during the day and you feel like you wanna do more. So yeah, total shift in thinking. You thought you were 100%, but you're really, probably not. Yeah, there's so much in there.   And it sounds to me, it also dimmed down and shifted your perspective on things, your ability to handle stress. Yeah, definitely, absolutely. I have a dog that just came in here, by the way, as I'm scratching my face, when I'm cleaning you down here like this, it's a dog. I've got two upstairs, don't worry. Don't assume, but this one likes to see her voices. So she may... Oh, we don't mind. We'll talk to him or her. I heard your dog show. So yeah, she's here, but if anyone has that feeling, it's probably true and you can probably benefit from taking a break. And I didn't really, even from the beginning, commit to being alcohol-free forever. I said, well, do the 90 days re-evaluate, just kind of like the dieting and see where I'm at with it.  And I thought that that was going to be hard for me. And I've been to now with the Fourth of July and we had a lot of birthdays that have been coming up as part of this through the Project 90. And you know what? It's really not that hard and it's not that hard to go out and be in a group. And I've still been a fun person, I was always fun.  You're just as much fun. Yeah. Drink, actually you watch people and you can be more fun because you're in control of what you're saying and doing and what you're saying and doing.  So you really do look at it kind of differently. For sure. Yeah, we talk a lot about alcohol and society and what Melissa and I are saying here, it's certainly no judgment on anyone. It's just kind of one of those things where you don't know what you don't know. I didn't realize how ingrained alcohol is into our society. You're right, everywhere we go, like, well, what are you drinking? Oh my gosh, it's been so stressful. COVID was so hard. We need to drink to get through it. We need to drink now that we're out of it or coming out of it. Like we got to celebrate. We got to blow off steam. Let's drink and you're right. You know, like when now you look, sounds like you look through a different lens. What are some of the biggest things you've observed in society and marketing? You really do. I mean, how they make it look so sexy. You have to have a drink in your hand or everyone looks really great. And I mean, the advertising, I mean, they're selling it. They're selling the poison, the attractively packaged poison. And as James says, and the smiling assassins that want you to come at you from everywhere. I think my first experience going out was with a couple of neighbors, a couple of women when we get together, we'll go out for appetizers and drinks and I said, sure. Let's go.  Oh, you have to have a drink, come on. Oh, come on, you have to have a drink. She kept saying it. I'm like, no, I really don't want to. And I just kind of blew it off. I didn't tell anyone. I was at that point in this project 90. I just said, you know, I'm trying to not be, I used my back sort of as a excuse and trying not to be inflammatory. And I just really didn't want to drink. And then we had a great time. And she had two martinis and that was fine. And I was kind of, it was funny. I was as much as I would go out and have probably two drinks when I would go out. It was amazing how I was concerned with her driving home. And my other neighbor only had one drink. And the one that was drinking kind of forced her to order a second one. And she didn't drink it, she didn't want it. And she took a sip of it, which I thought was pretty good. And I was kind of concerned for her driving home. And then I thought, well, I've done that a million times. For sure. I've done it a million times, but looking at her. So I said the next time I said, well, I'll be the driver. I'll be the neighborhood. Cause we live in the same neighborhood, but one was coming to work. One was coming from here, coming from there. So we weren't coming from the same location, but like I'll be the driver. And the other thing I've noticed on a positive note is how many people don't drink or don't want to drink. And I thought it was normal to go out and have a couple of drinks. And you know what, there are a lot of people that also feel like they just, maybe it's health. They want to be the healthiest version of themselves. They started working out and they feel someone said to me, well, I'm not going to, it's counterproductive to what I'm trying to do. And so I've decided not to drink. And I think you meet more and more people that are like, you know, we're not going to be, we're not going to be affected by all this advertising and what we're supposed to be doing and what, what looks cool or sexy or fun. I can be just as much fun with, I put in a wine glass usually in lime or some kind of fruit with sparkling water. And hey, the stores all have some really great flavors now like key lime or, you know, black cherry vanilla, orange pineapple, they're delicious. And it's sparkling water. I always like fizzy water.  But, but so that was a really positive thing that I noticed that there are people out there that a lot of people that I know that really kind of don't drink too much. Don't drink, yeah. Yeah, I think I just be cool or just sexy. Right. And, and, you know, when you're going back to talking about like coming home and, you know, keys on the counter, hair in a ponytail, glass of wine, that is simply a ritual.  This is what we do. And James and I talk about and suggest ways to recreate that ritual so that, yes, we are signaling the end of the day. It's relaxation time. And, yeah, a fancy glass, some, you know, rosemary sprigs or frozen fruit or whatever it is, so that you feel like, ah, I am having a treat. I'm having something special. But what are we really missing out on? Calories and inflammatory substance, you know, fogginess. And questioning if we should drive. I mean, gosh, have you ever read like how little it takes to be considered to impaired to drive, to drinks, to drinks. And you are over the legal limit. Yeah. That's pretty scary. Another funny thing. So, when I found out someone that didn't drink, my assistant at work, my in his 20s, very well put together, super smart. And he noted it, like they'll ask what we want at work and they'll actually order us whatever we want, drinks, snacks, not alcohol, of course. But so I was ordering a bunch of the different sparkling waters. And I had mentioned, I think, that I wasn't drinking or I really was trying not to drink. And he admitted that he had not had a drink in four years. He never had a problem. Uh-huh. A young guy, social life, you know, not married yet, going out. And I said, so, Kevin, why don't you drink? Why did you decide to give that up entirely four years ago? He's like, you know, I just found that I make better decisions in life. And I just thought, wow, for a young guy, we didn't have a problem to admit that and just voluntarily say, you know what? I think I'm a better version of myself when I'm not drinking. I was so proud of him. I'm like, that's fantastic. Good for you. Yeah, and you know, one thing about 2021 is, so we, of course, there's lots of divisiveness over certain things, but being an independent thinker is encouraged.  I believe this about this topic. So for those of you out there who think, well, I don't know, everyone I know drinks and how am I ever gonna navigate social situations? It's a good thing to go against the grain. It's a good thing to make your own choices, to make conscious choices. And that's what we do at Project 90. We don't say to anyone, okay, 90 days is just the start. You can never, ever, ever have a drink again.  It's not about that.  Yeah. You know what alcohol is as a substance now. You know what it does to our bodies and brains, even a little bit.  Our horse, I mean, around here. But the blinders are off. But the blinders are off and you can see it in society and how it's imposed upon us. And then the level of self, you see that, you know, I actually feel really comfortable without it. I feel good. And I would imagine that feels pretty empowering. It does. You know, I can set the example. I can be the ringleader. I can be the one that starts it and maybe people will follow without pressure, of course, because I know how I was and how, you know, and that wouldn't have bothered me because like I said, I wasn't someone who was laying in the gutter. Right. It wasn't that way at all. Just wanting to be that person that people thought was the most optimistic person they ever met. And I feel like when I was drinking, that wasn't me. It was me. I didn't wake up feeling like the most positive person. I didn't think I can be that as much. And maybe other people thought that even so, but I didn't feel it inside. And I felt like, I just felt like, you know, and with my kids getting to the point where maybe they're gonna have children and I felt like I was being destructive to myself. And I felt like, you know what? It's only a matter of time when all this adds up if I didn't have issues with my inner organs and body now, I will at some point at this stage. And if I kept it up, it's gonna have to affect me in some way, I thought. So I thought, you know what? I wanna live a long life. I wanna be here for them. I wanna enjoy the life that I have before I get hit with a major health issue. And you know that from going through cancer. I think it changes your mindset. And thank God I didn't have a major health issue to make me think like, wow, you didn't ding bell, like you did. Yeah, yeah.  And you cannot have this habit. And you know, the rest of your life is gonna be better.   If you're having one or two drinks a day or having one drink a day or three drinks a day, in some way as you age, you know, we're not 20 anymore or 30, it's gonna make a difference. And I just wanted to live a better life and felt that mentally, physically and every way, this is gonna help. And I think it has, I know it has. Yeah, yeah, it has, I love what you're saying. You talked earlier about how when you were in that habit of having the wine that, and I totally relate to it, you know, like whatever, something would happen in the day that would give you a reason in quotation marks to that wine. And when you come into Project 90, life still happens. Things go great and then some things don't go great. We still have stress. Talk to me a little bit about how that has shifted for you.  What's that experience been like for you when you're driving down the road and you're like, oh, today was stressful, this would have been, because I do that with myself, I'll have a day and I'll go, oh, this would have been a day where I would have had a real good reason to open that bottle of wine. What are those days like now? It's really funny. It's so hard to answer that. I do still have those days. And occasionally I'll say, oh, I really wish I could have, I'd really like to have a drink, or I really wish I could have a drink. And you know what? I really don't mean it. And I'll say that too. Mine is really, really, as we were out to dinner once and oddly out of habit, he was having a bourbon. He's like, I don't have, he's someone that has one and he's done. Yeah. I had one that I have to have two. Yes. He actually handed it to me to taste it. I'm like, what are you doing? Like, what are you doing? You know I'm not drinking. And he was like, oh my gosh, I didn't mean to. Right. But I didn't even want it, Victoria. I didn't even want it. And I do have the same days. I have the same stress. I have the same family issues or you know, your husband, or not even your husband. It doesn't even matter what it is. It could be like, you didn't make the green light. I don't know. I don't know. But something has shifted where I don't even, I don't think about that anymore when I come home. I don't want the drink. I mean, I know now that for now, I just say that for now, I'm going to stick with it. I don't think there's any reason for me to want to have a drink at a wedding, at a party, at a barbecue, at just, I don't feel the need. And I feel like I'm just as much fun.  Like it's just because you're having, it may be it's just natural high. I'm just having a good time, but it's funny, I've actually felt that. And I'm thinking, oh my gosh, I didn't have a drink and I'm actually feeling like kind of happy. And that will happen. I guarantee people out there it will happen and it's weird. But you almost feel like you have that buzz and maybe you're just having fun. Yes. And that's a big thing to talk about too. Like what are we, when we go to those bonfires, when we go to those weddings, when we come home after a long day at work and we want to unwind, what are we really seeking? Connection, laughter, relaxation, fun, making memories. Yeah, maybe trying to relieve that stress, but you know what, it's not really stress because it's only going to cause you more stress down the road. Like how, you know, is it going to be to try to not do this anymore? Right. And you don't need that stress. And this program is just, like I said, it's some kind of magic, but it does work. Yeah. And I went 90 days straight and I didn't feel like it was difficult. I didn't feel like I really felt like I was going to lose it any time. I never thought about it. And if you do, open up a mark of holo or reach out to a coach or there's always someone there to help you. And believe it or not, if a coach isn't available, there's people in the mark of holo that put themselves out there, call me. And I've done it too. If you're having a rough day, hey, reach out, reach out to someone because someone's going to help you. Someone's going to talk to you. Someone's going to talk you off the ledge or someone's going to say, what's really going on? What's really going on that's making you feel this way or making you want to have a drink? Because most times it's really nothing and it can be avoided. And it's something else you can do. It's a feeling. Yeah. And when you talk about connection and fun and laughter and memories, it sounds like what you're saying is being part of Project 90 kind of provides the things that alcohol promises but fails to deliver. Yeah. That sounds like a good point. Very true. Yeah. That's the real question. Does alcohol deliver on its promises? That's a good point. May get you to that feeling of the buzz, but what else?  Maybe you're nice to your children and not that I'm saying I didn't need that, but I'm talking about anybody. Like, what does it actually do for you?  I liked the taste of it.  I definitely enjoyed it. I enjoyed everything about it, but I'm enjoying how I feel and how I am more. Exactly. I feel like I have more control. I feel like I'm... Well, my kids will tell me I'm a control freak or I like everything just so. I'm very... So I'm in control now. I feel like I have much more control over myself and it's a really good feeling. Yes. It's a great feeling. And I love what you said about getting the buzz from the sparkly water. I'm like, am I really just drinking water? Yeah, yeah. What's in this? What's in this? No, I totally get it, though. And I love asking our members or seeing our members when they have that first really huge belly laugh on a call or something, or they're on Marco Polo and they're just lighting up and they're like, what is this? Oh my gosh. And they're realizing like, oh yeah, this is how we're supposed to feel. These are the natural highs in life. It is possible to feel without a call, definitely. And you'll sleep better and you'll be more productive and more aware. And you know what, after that party, you're gonna remember the good time that you had. Yes, right. Because you're having true connection with someone, not just blah, blah, blah over some drinks and not really connecting. And yeah, you're right. You remember everything about it. Yeah, honestly, everyone else was acting because they were drinking. Right, exactly. They won't be like, that's what you said. That's what you did. I know. I'm always like, oh my gosh, was I like that? Oh my gosh, I would. Now, I love that about being in control.  And we were just having a quote, good time, but it can be better. And we are at that age where we question things. And we think, am I living the best life I could? Is alcohol helping me live that best life? Probably not. Probably not, yeah. And if it's not, then come make some friends. Hey, you're making friends with a group of people with similar lifestyle, similar goals that all of us want a better life. Everyone wants sort of the same thing in the group. We're all after achieving the same thing. And if anyone's been involved, I've never been involved in any other programs for quitting alcohol. Like I've heard some horror stories about AA and people that have done that. And from what I've heard, this program is a polar opposite. It's not as positive and people sharing. And like I said, people with the same kind of goal. So everyone's trying to get to the same place of just having a better life and being present for your family and your friends and maybe just yourself. For sure, for sure. And being in a program like this, what I always say, people say, what's the difference between like this and therapy or AA or whatever? And I'm an advocate for all good things if it helps somebody do it. But in our program, we look at the past and we go, okay, this is what I was like. This is kind of what happened. And we go, okay, let's talk about today. Let's get the alcohol out of your system. And then let's look at the future. And that is so fun as a coach. And I'm sure as a member of our community to see that transformation in people, to see them come in and then they just, like I said in the beginning, the hair is shinier, the eyes are sparkling again. And they start to dream and they start to think big again.  Oh my gosh, this happened at work. And it's like, it's just magic. It is magic. It's so hard to explain how easy it's been. Yeah, it's just been the easiest thing. And so worth it. I agree. I agree. And something like this is not meant to be done alone. It's meant to be done with others. Definitely. Definitely. And that's been one of the main things what are the other people. The group that you meet in our graduating class has been the best. An amazing group. Just such an incredible group of people. Wonderful people, incredible people. Yeah, so much so that there's gonna be an international reunion. Yes, for sure. We're gonna do that, get that together. That's gonna be it. And go out to lunch and order a drink. I have a question. What would, what do you think, what would the Melissa before Project 90 think of the Melissa today? She would be very proud of her.  Cause I had been getting on James for years. And kind of reading them and look at the little videos and like, yeah, okay. And I don't know, something one day was like, bam, I'm gonna do this. And I went and had a serious conversation with my husband and showed him one of the emails and said, you know what? I think, I think I wanna do this. And he was unbelievably supportive from the echo. Like bam, just totally supportive. And so I would tell that Melissa like, gosh, why didn't you respond to, like I responded to the emails too even earlier and we had conversations but I never did it. We'd say why didn't you do it sooner? But I guess, you know, everyone has to do it at their own time and there's a right time for everyone.   But just, I think, yeah, I don't know. I just would be really proud of whatever you've wished. I bet, good job. Good job, yeah, for sure. Yeah, and this is, you know, you don't have to, it doesn't have to be oh so bad and you don't have to be ready, just start, right? Just start. Just do it. And you're gonna, with an amazing group who gets you and life is gonna change. You'd be so happy, you'd be so happy to eat. And not only for what it brings you personally, but like physically or for your own well-being, but the people and the connections that I think will last a long time. I hope so, I hope everyone stays in touch and we've been trying to. And yeah, it's the people that you mean, the connection that you make in addition to what you've done for yourself, you've created a whole new life of yourself physically, mentally, emotionally in every way. Yeah, yeah, just don't wait, do it.  It's like those listening to the Marco Polos on your way to and from work help you. And I certainly know that your posts helped others. So it's the ripple effect. And so those people, you listen to that on your way to work, so you are in a better mindset, a better headspace. You have no idea how that impacted the people around you, how they went on to interact with the people around them. It's just a great way to walk through the world. Yes, it is. And you can be that role model and maybe silently and slowly and not being overbearing, but just through your own actions. Yeah, it affects someone. And you never know who you're gonna affect, like even my assistant, just if someone coming forth and now creating a conversation and we were in a room full of people, just creating that conversation and I know people were listening. Yeah. You just never know who you're gonna affect. I know. With your positive attitude and you said then you're glowing attitude because you do that now. Yep, this has been awesome. Thank you for sharing your story. I know it's gonna touch other people. And what you're doing right now is going to affect other people's lives. And that is what we're putting on this earth to do. Well, thank you. Thank you. It's all because of you and James and Project 90 and all of the members. It's everyone's cumulative effect and I thank them all. I love them all. And we've all shared that with each other. And so thank you. I think it's saved my future. It's priceless. It is, it is. Thank you, Melissa. I just want to give you a hug. A hug. A virtual hug. All right. Well, have a wonderful rest of your week. And again, thank you for just being an ambassador of goodness and hope and positivity. Thank you. You're my pet girl. All right, thank you. All right, thank you so much. Thanks everyone for listening. Thanks for listening to the Alcohol Free Lifestyle Podcast. I want to load you up with some free stuff right now. So if you want to go to jameswanick.com slash guide, I will send you my quit alcohol guide which has helped six figure entrepreneurs and top professionals reduce or quit drinking. You can also text the word quit guide to the number 44222 if you're in the US, of course. It doesn't really work anywhere outside of the US. But if you're in the US on your mobile phone and you'd like that guide, text the word quit guide to the number 44222, or you can go to jameswanick.com slash guide. If you'd like to schedule a free 15 minute call with one of my top coaches, just an exploratory call to see if or how we can help you, then you can go to jameswanick.com slash schedule or you can text the word project 90 to the number 44222 if you're listening in the US on a mobile phone. That's jameswanick.com slash schedule or you can text the word project 90, that's one word, project 90 to the number 44222. Feel free to send me a direct message over on my Instagram account which is at jameswanick. You can also watch video episodes of this podcast and a series of other educational videos on my YouTube channel which is jameswanick.one or you can direct message me on Facebook at jameswanick.official. And finally, a request. Would you please now write a short review of the podcast inside of the Apple podcast app on your phone or on iTunes on your desktop computer? Would you please give the show five stars and write a quick one or two sentence review? This will help the show get in front of even more listeners, potentially transforming someone's life. You can rate and review the show inside of your Apple podcast app on your phone or over on iTunes on your desktop. Thank you so much and I'll catch you next time.


Welcome to ToffeeTV, it is the Everton News Daily. Sasha Ryan-Sav has said that it will take several years for Everton to move from Gooderson Park to Bramley Mordoch. He was speaking at the Leather Sports Business Summit at Stamford Bridge today and said he hopes that the stadium will close the gap on the top four, top six. He said it'll breathe new life into the city. It'll create one billion pounds of income into the local area. He said it'll create jobs and it'll breathe new life into the club and the team as Everton look to become amongst soccer's elite in the Premier League. Listen, you can interpret several years anywhere you want. Everton want to be in there by 2022-2023 compared to next year, that's several. So it isn't really much of an update but it's good that the club are now talking about it. Obviously Dan Mice is on Mersey side today. So I'm guessing soon we should be seeing some pictures maybe or images or concepts or an update of some sort. You know we've been to U1 for a while and I believe that one probably isn't that far away now. The pieces are starting to line up and hopefully it won't be too much longer before we get an update which will you know I suppose will keep everybody happy, won't it? Now if they could get one out during the international break that would be the perfect time. I would suggest to to get it out and keep the the good feeling going obviously after back-to-back Premier League wins. Luka Dan has spoken about his delight of being back in the French side and has thanked Everton for enabling him to get back to his best form. He said he settled in really well to life on Mersey side. He's enjoying playing for Everton and it's only because of Everton that he is back in the French national squad. Him and Caret Sumer of course being pictured over the last few days training with the French national team. We are of course well-cut winners, the well-cut holders and I think it's great for Everton to go on forward to have people like Luka Dan and Caret Sumer getting in to their national sides because it shows a certain level of play that if they're not regulars in their team but they're at league clubs that you know will move to Everton doesn't mean you can't progress in your career and doesn't mean you can't be rewarded internationally. You know and in turn that helps us as we try to bridge that gap and make our team better. You know and Luka Dan and Caret Sumer have certainly done that since they come in so hopefully it's the case with the likes of Andre Gomez and Yeri Meeneer as well when they get in they'll be back in their national sides and then again Everton's name gets spread around and players can see what's happening with them you know when it makes the whole club more appealing because obviously you're looking for anything when you haven't got the likes of Champions League football or whatever it's appealing if players can look and think you know what I can still progress at that club and I still can be seen and still called up by my national side so good luck to all of our players including the likes of Richard Jarlison and all the young lads you up in Pickford and all the young lads who are away with their national sides. Christian Ben Teche has undergone minor surgery in his knee. Crystal Palace said he's expected to return to training in a few weeks so it is very very doubtful but it's probably out of the Everton game so that is good for us because he's still awkward whether he's scoring goals or not he's still a handful and normally has a decent game against us so that's good news ahead of that Crystal Palace game and Karen Dahl is 21 today so happy birthday Karen he's also been linked with a move to Bristol City on loan there's a lot of quotes from Bristol's journalists saying that they're very interested in taking him and a few Twitter comments and comments on social media from Bristol City fans raving about seeing him at Nottingham Forrest last year and would love to have him in to their side so it'll be interesting because he's played a couple of Carabao Cup games but we're not in that now and you just wonder if going out to Bristol City on loan again might benefit him rather than them staying around the first team the periphery of the first team and playing 23 games I don't know we might not want to go out a game but you know there's certainly an argument and a case for him going out for the second half of the season to Bristol City and just getting that regular football again and maybe doing a little bit more in the games getting used to being involved in the games a bit more and finally it is World Mental Health Day some Everton senior officials have undergone some training regarding that but it was a fantastic piece on The One Show last night it's on our Twitter feed and I think our Facebook page as well if you haven't seen it get over and check that out it was a brilliant piece run by The One Show and just showing the work that evident in the community does absolutely fantastic you know and helping people who have suffered from illness in their lives or lost partners just a couple of initiatives that the club do evident in the community do they're absolutely fantastic they really really are and that's why you know Michelle from Pedder trying to get involved as much as we can in raising money for them as well because it when you see it like that it's one thing I suppose being on the Evan website but when you see him on a national news programme and you see the response from other people as well about it it really hits home what fantastic work they do in our community and for our city you know and you know I was it was proud I was really proud to see that and to see that you know football clubs are very good at taking and have took for a long time and us as fans we we go to match and you know we support our team and it engulfs our lives but it's great when something can be given back to people who need it and I just think you know me and Pedder over the last few weeks have spent quite a bit of time down in the community and the hub and stuff so you can just see what a fantastic project it is and they do projects all over the city so if you can't keep you know help them any way you can it might be by donating to our to us to do as if buying or it might be getting involved yourself in the sleepout which is next month it might simply be going in and saying you know spend the money in the cafe maybe or going in and volunteering and just saying what can I get involved with if you've got some spare time because you've just seen last night with your own eyes the fantastic job that they do in the community show a massive massive part on the back to all involve the revenue in the community it's a fantastic aspect of our football club that's it for the news daily give us a subscribe if you haven't already if you want more videos get over join us on page and 10 exclusive shows a week now on page and as well and otherwise have a great night see you later on toffee tv


Hi everyone, I don't want to assume that all of you are familiar with MacBook Pros. And so we're going to do a quick overview for those of you who might not be. In front of you you have a 13 inch MacBook Pro and it has the iMovie software on it that we're going to use. The computer might be assigned to you alone or to you and a partner. Either way, next to your keyboard on the top right is a small circular button that will turn on your computer. We'll have each of you turn it on in a second. Each machine has a login and password taped onto a piece of paper next to your keyboard. So find that tape piece of paper to know what your password and your login is. Okay, so you found the piece of paper. Go ahead and turn your computer on. So all the computers you'll notice are fully charged. Well, how do you know that they're fully charged and you don't need to plug in your computer? There's a battery picture or what I call an icon located at the top of your screen. If the battery is fully black, then the battery is fully charged. And if it's almost entirely empty, then your battery power is almost zero and you'll need to plug in your computer to recharge. So keep an eye on that from time to time. Another thing you'll notice on your desktop is the dock. And this bar right here is the dock. You can control where you place the dock on your desktop. My dock is on the bottom of my laptop here, but I usually like it on the side. So in later videos, you'll likely see my dock in different places. The more important question is what does the dock do? Well, it holds pictures or icons that you can click on to open various software programs. I can also add or delete icons too. And you should know that you're able to do that and personalize your own dock. We are not going to do that in this class, but know that you can do that. The purpose, the real purpose of the dock is to help you work fast. And it puts access to software programs right on your desktop right when you open your Mac. Another thing that you'll notice is that we're not using a mouse. Instead, we have a trackpad just underneath our keyboard. And that's that rectangular square. With the trackpad, you can control and direct the cursor or arrow on your screen.  You'll see that it tracks your finger. You can activate your cursor or the arrow by pressing down on the trackpad. There's actually a lot of gestures you can learn to manipulate your trackpad. And that's a story for another day. So next really quickly, let's take a look at the sides of your computer and what you'll find there are the ports or the connections. The first port is the MagSafe port for power, a power cord. Then an Ethernet cord can be connected in the next port to connect to the Internet. Then there's Firewire connects to things like cameras or video cameras. After that is Thunderbolt Thunderbolt's proprietary meaning that only Apple products use Thunderbolt and they allow very fast connections. Following that is USB ports to connect to things like hard drives. And then there is an SD card reader for things like memory cards that you can use in cameras and video cameras or you can capture music and finally a headphone jack. On the other side, there's a port for a drive, a super drive for things like a DVD with a movie or music. And there's a little port for a lock as well if you have one. So we're going to take a break here and I'd like to know what have you learned so far.


Hello folks today, we are going to understand how do we represent irrational numbers on a number line? Okay, so before we start we first Understand what is a number line? So in your previous grades you would have studied that if I have a line I Can I can represent all the numbers on a number line, right? Let us say this is a line and we can represent all the numbers known to us on a number line So far we have dealt with natural numbers whole numbers integers and Raster numbers is it it so we will see how do we represent these numbers? so how do you start to draw a line and Then at any point let us say this point is Point zero right and then what you need to do is you just take one unit length Let us say one centimeter or half a centimeter as a unit and then graduate this line or Divide these lines into equal parts like this like that. Okay, so Actually, it is done through a ruler and a Pencil or a compass right so hence you can draw a straight line Then you can mark the point zero and from there both on the right-hand side and on the left-hand side You can divide the lines into small small parts such that each part is of same length So hence all these points which I have drawn represent one two three Four and so on and so forth right all these points are Integers here also it is minus one minus two minus three and so on and so forth Isn't it now if I have to represent point five so where would point five be so, you know, it's very Easy point five is nothing but between zero and one exactly at the middle point So this is this might be point five and how do I? Geometrically do this so far for that what you need to do is you have to take The needle of the compass on any of these points Let us say this point and from there you roughly measure more than half the distance between These two point okay, and then from here here you draw an arc Similarly from this point you draw another arc with the same radius and you repeat the exercise on the Bottom side as well and then you Connect, you know, this is called bisecting the line segment right so wherever this dotted line meets the number line Let us say this point will be nothing, but this is zero point Five is it it now? Let us say if I have to represent One upon three one upon three. How do I represent? So let me draw the Number line once again and this time around I'll take a bigger scale. So let us say this is my Number line and this is zero and for the convenience sake, let us say this is one Okay, and I have to draw one by three So you know how to do it. So you simply draw an inclined line on zero and then you join whatever the end point is Here to here. Let us say and you have to you have to draw this O Let's say P in such a way that you can divide this line into three parts So let us say you take OP as six centimeter Why because six is a multiple of three so P is equal to six centimeter you take Then what you do is you? mark Points like this so that each division is of two units. So like that Let us say you have In you using a scale or a compass you can you can Mark two points such that this distance is to this distance is to and this distance is to as well right then what you need to do is and Once I will finish the construction, then I'll explain how and why we are doing it now Let us say this point is a now you join PA and And from all these points, let us say this is P1 and P2 you draw P1 a1 Parallel to PA and P2 a2 parallel to PA again, so if you see these are nothing but equal parts of Equal parts of OA okay divided into three parts. So hence this point will be nothing but one upon Three this is how you can find out a fraction between two points Or let's say between zero and one okay one upon three. So basically I divided this segment OA this segment OA into three equal parts using the construction So the first part is one by three. So automatically if you see this second part will be Two by three. So this part is two by three this point is two by three. Okay. This is how rational numbers are plot on a Number line. Let us now move on how to plot Irrational numbers, you know irrational numbers are nothing but numbers of the form of sorry numbers Which cannot be expressed in the form of P by Q numbers which cannot be expressed in the form of P by Q Is it it so let us say I have to represent root 2 root 2 on the number line root 2 is a irrational number. This is an Irrational number isn't it? So how do we represent root 2? on a Number line. So please note that a number line Contains all the real numbers hence it is also called a Real line we can represent all the numbers on a real line now it starts with let's say zero all integers Anyways, we know that they can be very well expressed on a real real line similarly all Rational numbers also we just saw in the previous case. So this is one two. Let us say three This is minus one minus two minus three. So if you see all the points all the point On the real number line will represent a particular number whether it is rational or irrational We just saw how to find out half one by three on the number line now in this case We are going to learn how to plot root 2 on the real line Obviously, it will be very difficult to do with a ruler and a scale even if you know the Approximate value of root 2 so hence we use geometry to solve this or to find out where exactly root 2 Will be lying on this number line I hope you know that all these numbers are nothing but all these numbers are represented by Points on the number line. So let us say root 2. So we will use Pythagoras theorem to find out root 2 on the on the Number line how so let us say I have to find out root 2. So I will take this one unit here From 0 to 1 and then I will draw a perpendicular On one such that let us say this point is o this point is a and this point is b we have to make sure that oh a is one and a b a b is One okay. Now you join ob Okay, so what do I know about ob so Basically ob square is equal to oh a square Plus a b square isn't it? Why because of Pythagoras theorem. So hence if it is one square, sorry, this is one hence if it is one If it is one then this is nothing but root of one square plus one square, isn't it? Which is nothing but root of 2 isn't it? So hence we say we say equal to one square plus one square and by geometry Ob is equal to root of 2 right now you take the needle of the compass and put it on oh and Take the radius equal to ob and try to draw an arc such that the circle the radius Oh, sorry the arc cuts cuts the number line at let us say point p Okay, so since ob is equal to root 2 and we are drawing a circle on an arc with radius ob So op also is the radius of the same arc. So this is also root 2 So hence eventually we are able to locate where root 2 will be on the number line. Okay, once again, so you draw Segment of one unit draw a perpendicular segment of one unit so that the hypotenuse becomes root 2 and hence if you draw the arc cutting the Number line then the point where it meets the arc meets the number line is the irrational number 2 Let us now say we find out we want to find out root 3 where exactly root 3 will lie So again, I have to use the Pythagoras theorem. So let us say this is 0 Okay, and you draw you draw And we know that these are the points 0 1 2 on the number line We just found out root 2 how to find out root 2 you draw one unit perpendicular on one then join these two points and Take the arc. So wherever the arc cuts is the root 2 value now This this length is root 2. Is it it now? Let us say we want to we just put another A perpendicular over root 2 point and now join these two points. Let us name them So let us say this is a this was B.  Isn't it? So what will OQ be? OQ is root of 3 Right, so if OQ is 3 we'll repeat the process and let us say you draw this Arc like that. Okay, so this point is Root 3. So this is how you can locate any irrational number on The number line will take up some more example in the problem solving sessions