Hello, everyone, and welcome to our Ask a Psychiatrist livestream. My name is Monica, and today I have the honor to chat to Dr. Bradwin about depressive disorders and what we can do to optimize our wellness. Specifically, in the first part of this livestream, we'll be answering questions that you sent in through the community and through the Discord server. Then we'll have the opportunity to talk about ways to optimize wellness using the intrinsic practice, which is a psychological literacy program that you can use to enhance your experience of happiness. So I invite you to deeply engage in our chat today by leaving your comments, thoughts, or questions in the chat box to the right, or a comment below. Enjoy. As well, I do want to remind you that because we are touching upon potentially sensitive topics, to take the time you need to take care of yourself. This recording will be available for you to watch at your own convenience, so there's definitely no pressure to watch it now, though we do welcome you to join us live if that's something you're comfortable with. So the plan for today is that I will give a brief introduction to myself, Dr. Bradwin, and then we will jump directly into the questions that you've sent in from the community, followed by the ways that you can use to optimize your wellness. It's well because I know that many of you are joining from different parts of the world at different times. I'm going to be repeating the outline periodically throughout the live stream just so you know where we're at. And so with that, thank you so much for tuning with us today. We really appreciate it and we hope this helps increase the accessibility to psychology and psychiatry. So my name is Monica and I am a clinical neuroscience graduate student with a strong passion for psychiatry and outreach initiatives. Very, very grateful that I get to participate as a Psych2Go team member, where I get to talk to you, the community, and chat with experts. So with that, I'm going to give you all an introduction to our expert today, Dr. Bradwin. So welcome, Dr. Bradwin. Hi, Monica. Hello. Thank you for joining us. So Dr. Bradwin... Nice to meet you back. Yeah, Dr. Bradwin is a psychiatrist trained in medicine at the University of Sherbrooke and psychiatry at McGill University. He is a professor emeritus and ex-dean of medicine at the University of Ottawa, founding dean at the Ottawa Shanghai Joint School of Medicine. Visiting professor at the Shanghai Jiao Tong University School of Medicine and is presently a professor of psychiatry at the University of Montreal. His work has been shared in over 350 educational media interventions and his specialties are in psychotherapy, medical education, and psychiatry. So he truly brings expert advice to today's discussion. Psych2Go hopes to host more of these educational media interventions to make psychiatry and psychology accessible to all. Welcome, Dr. Bradwin. Thank you. I'm glad to be back. Very, very happy that you're able to be back. I'm sure a lot of people enjoyed watching our last live stream about anxiety, which you can find on our channel. So I thought, let's just begin with a question that really puts this whole live stream about depression and depressive disorders into context. And this is actually the most commonly asked question on our YouTube community. So someone has asked us to provide an overview about some of the types of depressive disorders and the common signs to look out for. Okay, so the basic question is what is depression? I think it's a good first question. So depression simply is when generally we feel low, everything is slow, everything is dark, everything is hard. So at the level of our body, we may not have much energy. We may not have much appetite. We can't sleep much. We may have also lots of aches and pains. And then emotionally, either it's empty. We feel empty. We feel sad. We may feel a lot of guilt and some irritability. In terms of our thoughts, difficulty concentrating, keeping attention. We think slow and often we think in a very pessimistic way, even thinking that life is not worth it and thinking of hurting oneself and so on. And also behaviorally, we tend to isolate. We tend to not feel to do things, not want to do things, not meet people and isolate. And generally our self-esteem is low. We don't feel very good. So overall, that is depression. It's also called major depression, major depressive disorder. It depends what the dynastic systems that are used. But basically it's depression. So that's the experience of depression. And then there are different types of depression. So some that are just calm, went and go. So it's a major depression, one episode. They are some depression that tend to come back. So meaning that they last a few months, they're very painful, but things get better, things get normal. And then maybe a few months later, a few years later. Another experience of depression. So this may be called recurrence, recurrent depression. So meaning that they come back often. There's also a type of depression, which is similar to major depression, but not that intense, but always there. So it's a depression that is milder, always there. And so sometimes it's called dysthymia or persistent depressive disorder. So it's not like a down and then back up and normal again. It's always a bit down, always a bit having to push oneself to feel good. So it's always there. So it's a persistent type of depression. And then another type, which is very important to see the difference is that a combination of major depression, so when everything is low, dark, slow, but then with episodes that everything is the opposite. Everything is high, everything is bright, everything is good. So for example, the opposite of being tired, lots of energy, the opposite of being sad and being euphoric, feeling on top of the world. The mind goes very, very, very quick doing a lot of things, often socializing a lot, spending a lot of money. That's called hypomania or mania. And in combination with major depression, the low and the high, it's when you hear about bipolar disorder, basically bipolar disorder. It's a bit of a different type. Oh, wow. That's really useful to know. I think a nice follow-up question is that once people notice these signs of having trouble sleeping, low mood, and things that are typically associated with depression, how would you recommend someone to prevent this from spiraling or getting any worse? Yes, well, the usual is to seek professional help to at least get a good evaluation to make sure that it is depression and to understand how it became depression. Why? Why? In myself, why am I depressed? So then with a good evaluation, it's possible to determine, do I have a family history? Does depression run in a family? Or is it depression plus bipolar illness? That's important to know. So is it also because of some of my psychological habits that contribute to it? I have attended to isolate myself that would contribute to it. So a good evaluation will determine partly the cause, so the biological cause, the psychological cause, and the social cause, and confirm the diagnosis. So that's the first thing to do. So then based on that, a good treatment plan can be devised. Because a good treatment plan, and they are very good treatments, many work very well, but it has to be well, well tailored to each individual. So that's why a good evaluation is the key to get a good treatment plan. Right. And for those looking to seek that professional treatment plan, who do they typically go to? Are they therapists, psychologists, psychiatrists? Do you mind breaking that down a little further for our younger audience members who may not know? Yes. Well, at first, it may be any primary care professional, often family physician, or sometimes at school. It could be health services, student services for to get that first evaluation. And based on that, then it could be more access to either a psychologist. If the main treatment will be psychological, it could be also the family physician, whether psychologist, if there needs to be medication, if there needs to, in addition to psychological treatment. Sometimes the diagnosis is not clear, or treatment has been suggested, but doesn't work quite as well as expected. So there may be a need for a consultation with an evaluation with a psychiatrist, so go deeper into what may be the diagnosis that causes and more suggestions for treatment. So it's a continuum. But first, reach out. It's to reach out if it's at schools, student services, primary care system, some mental health community centers, depending also where one lives and how care is organized. But it's to reach out and then eventually there can be access to the proper help, and eventually more specialized help if necessary. Great, that's very useful. It is another point too, that if one feels so bad that everything is so dark, everything is so painful, that life doesn't even feel worth it anymore, and having ideas of death, ideas of hurting oneself, ideas of suicide, then any emergency room, or in some places there are some crisis lines by phone that can be reached. Sometimes there's a system with a mobile crisis team or the emergency room, because then it could be right away a good evaluation and a good access to services, because it's serious. It's like having any other medical problem that may be very intense, very acute, have to get the care right away. Yeah, it's very good to speak to the importance of reaching out as soon as one notices some signs that can become quite distressing. But I do know that many people who commented in the community said that it's quite difficult to get that courage or even have that access to care, and so what are your thoughts or advice for that, for people who cannot not necessarily reach out? Yes, well you're quite right, because part of the experience of depression is losing hope, feeling hopeless, feeling helpless, feeling that things won't work out, not having trust, and not having much energy sometimes to do things, so it's very hard to reach out. But that's at a time where at minimum call, call a friend, call a family member, if your student just go to the school health center or sometimes to employee health, reach out. I know it's hard, but that effort is really necessary, because there's no hope when we're depressed. So we don't even think about things that may be able to get better, that there are some good treatments, that things could go well, that there's a loss of perspective, that things were well and they'd get well again, because it's the moment and it's painful and it's dark. So it's to have a bit of hope, have a bit of trust, and reach out, reach out. For sure, yeah, hope is a really, really big part of it, and on that topic of kind of factors that can improve depressive symptoms or factors that can hurt it, would you like to talk about the kind of beneficial things to do or personality or like attitudes to have versus the not so beneficial ones that can extend the experience of depression? Yes, so during a depression, so we're talking more about treatment, right, treatment, because it's serious, it's painful and something needs to be done. So in the same way that we may understand depression and the various types of depressions as a biopsychosocial suffering issue, right? There may be some biology, the way our body functions, our brain, there may be some genetics, some psychological ways that we have that may not be very conducive to feeling well and social isolation, then the health is also along the biopsychosocial dimension. So what does bio mean? Sometimes it means a bit of behavioral activation to do a bit, to start to do a bit, even if it's walking a bit, even though it's very difficult, but to be a bit active, eat well, avoid as much as possible substances, alcohol, because it can worsen problems of depression and medication may be necessary. So there are many different types of medication that can help a lot. So that's the biological aspect of it. Psychologically, there are therapies that have been shown to work very well to be fictitious. So we talk about cognitive behavior therapy for depression that can work very well. So modifying thoughts, dark thoughts, but also some of the behavior and also the emotions. So cognitive behavior therapy or CBT. There's a form also of therapy that is based on life transitions and relationships called interpersonal therapy. IPT is also a very good technique. There is some what we call biological activation. So there are many tools, many tools that can be useful to really get out of the depression. The social aspect of it, biopsychosocial, the social aspect of it is very important because when we suffer from depression, even from anxiety, there's a tendency to do less socially. There's a tendency to isolate and have less social contacts. That in itself becomes a problem because it's like a deprivation. So it causes harm to be alone and not to connect with people we like and people we feel good with. So that social isolation has to be reversed in a sense to reach out to do more. That's part of the treatment. That's part of the treatment because social contacts, social activities, network, it not only feeds wellness but it can also help during recovery, biopsychosocial. So the whole it's a whole package really of interventions that can be used and done to get out of depression. Yeah, that's definitely very good to know the vast array of tools that are available. And on that topic of treatments, are there any specific kinds or like combinations that typically you would recommend someone to seek out? Or do you think that people should just be open to whichever their practitioner recommends? Well to be open to whatever the science has shown, whatever we know works. Many clinicians such as myself see the beneficial effects of treatment, especially a well-tailored complete treatment, biopsychosocial. They work, they do work. So one that is recommended to trust, to try. Medication treatment, there are many medications that can work well. The key is to choose them well. The first medication to adjust medication well, to set the goals and combine it with psychological tools. So sometimes the combination and depends on the people, on the person's wishes, sometimes it can be a combined treatment. So person says, yeah, I'm depressed. I don't mind taking medication. I want to get out of, I suffer so much. I'll take medication. And I also want to try the psychological tools that you may offer to me and I'll do my best. So I'll take the whole package. So it's like a combined treatment. Sometimes people prefer to start with medication. And after that, maybe use more of the psychological tools, take the medication and wait for things to get better. So it's more sequential or the other way around. I'll start with depending on the urgency and how deep the depression is. Some people will say, I'll try without medication, like cognitive behavior therapy or interpersonal therapy, for example. And that may be sufficient. That may work. But if it's not, then medication can be added. So it's sequential, one after the other. So yes, so to trust, to believe, because trusting and believing and trying gives a good chance of getting well because these treatments can work very well. Great. And when you say work, do you think someone can expect for their depression to fully go away or for them to just expect a reduction in their symptoms so that they are now functional? What kind of outcome are we kind of? Yes. So it all depends on the person. It all depends on how many depressions, so if it's recurrent and how life habits were. But setting goals is very important. And so there's the goal of betterness. I want to get better. So less symptoms, less sadness, better sleep, eating better, having more energy. That's good. That's good is to come out of the depression. But it's also always good to say, I would like to go beyond betterness. I would like to be at wellness. And then at this point, it's more, I want to be well. And what can I do? The way I think, the way I feel in my relationships, in my life, what can I do to not only get well, but stay well. So that's when any good mental health practice, whichever you like, is good to not only stay out of depression, but continue to be well. So goals are very important. At first, it may be betterness. But at some point, one has to decide for oneself, do I really want wellness? And what do I want to, what am I willing to do, right, to stay well? Because at first, it's hard. It takes effort. It takes some discipline. As things get better, then it's simpler to organize one's life when we're being, as a path of wellness, as a path of a good mental health wellness through good practices, psychological practices, a good diet, good exercise, doing a bit of mind and body exercises are many there. So that, that maintains wellness. That's awesome to know. Just for those joining us today, or just joined us, because I see a couple of people have just joined. We are doing a live stream. My name is Monica, and I'm joined with Dr. Bradwin to talk about depressive disorders and ways to maintain wellness. And on the topic that we were just discussing, we'll be talking about ways to optimize and enhance one's experience of happiness later on the stream. So make sure you stay tuned and listen to that. So now we've already just covered the general kind of basic understanding of depression, depressive disorders, and I thought it might be a good opportunity to answer some more specific questions that the community has asked. How does that sound? Yeah, sounds very good. Awesome. So a user by the name of Yellow Mellow on YouTube has asked, why can a person experience feelings of being depressed when there is no obvious reason for it? In other words, it just seems to come on suddenly without an obvious explanation, making it harder to really identify a root cause. Yes, because, and again, the concept of biopsychosocial can be useful because when may have a nice personality, grew up in a nice family, having a good childhood and things coming easy, good environment, let's feel depressed. Why? Because there can be a predisposition or it can be a biological vulnerability or sensitivity that can lead to depression with no obvious, obvious causes or triggers or traumas and so on. It can be a biological bite. Anything in the body, including the brain, can at some point not function well. So it could be the lungs, it could be the pancreas and so on and so forth. And it just, it could be a biological predisposition. Often we see when we do a good careful evaluation, the background that depression runs in the family on both sides of the family. So it could be some genetic vulnerability and predisposition and then can lead to depression. And obviously, if on top of that there may be a difficult childhood, there could be a difficult circumstances, poor lifestyle, use of too much alcohol, substances, then it can make the biological predisposition of vulnerability worse. But a person can lead a very good and healthy life and still get into a piece of depression. Yeah, that's very interesting. You mentioned the biological component and while interacting with the psychotrago community, I noticed many of the users were curious as to know, what exactly are these biological components? Would you like to go into perhaps a little more depth? Yes, yes. So it's basically regions of the brain. So the emotional region of the brain, even the more thinking region of the brain, but also what we call the regular function region of the brain, so that body energy, sleep, regulation, appetite and so on, they can be a dysregulation. It can just not work as well. There are many hypotheses and some scientific evidence that in these regions, and we speak, it's very complex. The brain is extremely complex, but they are what we call neurotransmitter networks, the way they work together at dysfunction and then can lead to these low mood, dark mood and thoughts and so on. What are neurotransmitters? Well, the way the brain functions, roughly, is that there are millions of nerves that communicate with each other. That's how we live, that's what we live, what we experience, what we see, what we think, how we move and everything. The nerves, communicational nerves, often by releasing a substance, natural substance, that activates or inhibits the next nerve, so that these are neurotransmitters. In depression, it is postulated that some of the system are not as well balanced. It's not just one neurotransmitter or two or three, it's many of them, but it has to do with the whole fine tuning of the system. It doesn't work as well and leads to some symptoms of manifestation. It can be depression, it can be anxiety disorders, like we have spoken about during the last event together. This can be a dysregulation. The treatments, biologically, tend to act on these neurotransmitters and the nerves and rebalance them. That's why we speak about medications that may act a bit more on serotonin or adrenaline, dopamine, and so on. It's very complex. They're just to simplify. They do work. They do work and they have actions in these areas of the brain to these neurotransmitter systems. We also know from doing, for example, imaging studies. We're being able to see the brain, but also see the activity of the brain. Before and after treatment, it can be changed in these regions of the brain. What's interesting about treatments that work well in people who have depression, for example, medication treatment, psychotherapy treatment, when a person gets better, either from using medication or psychotherapy. There is a study done before and after treatment. Before the treatment works, look at the brain activity in the regions and re-measuring after. They are well, true treatment. There are changes. The brain is different. What's also interesting is that quite often, the changes that are activated by medication are different than the changes that are activated by psychotherapy. At some time, a combination is best because they don't do exactly the same thing at the same place in the brain. It's very interesting. I've always been quite interested to learn about the biological basis of how that works. Since we have a lot of questions about social aspects of it, I think we'll save that. We'll put a pin on that, and then we'll talk about the social aspects. For instance, Rochelle from YouTube has asked, how does one deal with depression if they are living in a highly stressful, fast-paced environment when there is really no time to rest? Really tackling the social aspect of the biopsychosocial model. Yes, there are several aspects to that. During a depression, it's hard to cope. It's hard to cope with life demanding. Sometimes, the life is very demanding, but we're well, and we cope with it, and we like it, and we do well. During a depression, it's hard. Sometimes, the environment is difficult, the work environment is difficult, the school environment or life in general is difficult. That's even harder during a depression. There's also how we see things, how we react to things, how we give interpretation to what happens to us. That's when the notion of the locus of control can be very important, which means that some people tend to react from the environment. They're more outside in type of people, and so they tend to be more affected by what's difficult in the environment. Other people tend or learn to be more anchored into themselves, into calmness, into confidence, and they act more on life, so they don't react as much. They're not as sensitive to things that may be difficult. Learning how to be more from an internal locus of control, so the power inside, I use it, and I live from the inside out, can help a lot in general and help a lot during depression, but can also help a lot in not getting depressed. There's also what we call a thinking mediation. When something happens or the way we look at the world, the world being more pessimistic, coming to the conclusion that things will not go well, are not well, losing perspective in time or even in space and only seeing the bad thing and not being able to see the rest of it, so it's a way of understanding and processing, so these are cognitive processes, negative, cognitive sets, we can say that can influence more and more the emotions and lead to depression and make it worse. There's also a certain type of emotionality. If we tend to be sad and angry and react a lot from anger rather than to learn to be more calm and also optimistic or use a bit of courage, the negative emotions are experienced during depression, but negative emotions themselves can maintain or worsen depression, so that's the emotional aspect. Then there's the interpersonal aspect and what we were saying earlier is that during depression we isolate, if there's stress we might isolate, not contact friends or family and then suffer from that isolation and that reinforces depression and even contributes to it, so one of the ways out is to reach out, connect with people, consider connect more people who we trust and we feel good with and sometimes the techniques of interpersonal psychotherapy is to make these relationships better, more conducive to feeling well and so these are all the approaches in the sense of feeling better. That's awesome. I think especially these days where isolation is unfortunately quite prominent due to the COVID-19 pandemic, it has become more and more difficult to reach out and gain that in-person contact, so do you have any advice for being able to stay connected for those who don't really feel as connected through the screen, for example, because I know it's a quite common experience among students. Yes and it's been especially hard, it's still hard now during the pandemic, but even to the screen that's better than not being connected at all. Simple walks, getting out of the apartment, getting out of home and meet people on the way and now there's more and more possibilities to go back to cafe and have some activities outside. This is very important. Some people during the pandemic have taken the opportunity to reach out to cousins that they like, that they don't have much chance to see because when things were very busy they never, so to family, to do family reunions, friends, because we have at least some tools to connect virtually, which is something it's important. Joining groups sometimes activities, especially as the pandemic things open up, but sometimes when there is a reach out for help, part of the help will be some group activities, because the psychotherapy could also be in a group psychotherapy, group CBT for example, that can be helpful. But good social contact, more social contacts, that will help during a depression and because during a depression we do less, we see less people, we're less connected and that in itself becomes a problem, contributes to the depression because it's a deprivation in a sense of social contacts. Yeah that's very good to reinforce the main idea that any contact even through this screen is better than just kind of closing, closing in on oneself I think, that being the message. And yeah so that is essentially one of the main three questions that we've received from the community about depression, really focused on one's own experience. We also have questions that were focused more on how a person can help their friend for instance, so before we go into those I just wanted to give another recap of what we've covered for those that just joined in. So we've talked about depression overall, we've covered questions about that, then we talked about more specific questions sent from the community about the experience of depression. We are going to then talk about the ways that one can support a friend or a family member for who's experienced depression and then finally we're going to talk about ways to optimize wellness and questions sent in from the chat. So if you haven't gotten the chance be sure to send questions in the chat and we will get to it. So with regards to social support, Jax from YouTube has asked, social support is very important but how do you help someone that's going through depression but their attitude is unhealthy for those around them? Yeah so first is to understand, we spoke about the symptoms and manifestation of mature depression to understand what it is and if you suspect that your friend or family member may be experiencing depression well it's against to reach out not to be to push in a sense but just to reach out to see what the problem may be, ask how one can help try maybe to encourage more connection but then it comes at some point where you know it could be serious and it could be urgent so especially if there is talks about you know not enjoying life thinking about dying even talking about suicide then as much as possible to encourage to seek out for help sometimes it's necessary to you know take the measures to make sure that they just access to help going to an emergency room and going with that person and a friend to an emergency room encouraging and even going and physically and helping because it can be very serious you know thoughts of suicide but otherwise is to try to be there try to support and also encourage seeking for help you know giving example of maybe know somebody who's who went to a rough time or yourself and did get help and it was it was good it was helpful point out where help may be available and encouraging staying in contact in contact because isolation is the worst yeah I think providing that kind of personal anecdote or the anecdote of a friend if they have permission to do so can be really helpful to encourage a friend or family member to reach out for sure yes and sometimes doing a bit of the information gathering of where it helped to be that could be simple and suggest you know that there are ways and here are the phone numbers or the addresses or where when you could reach out you know it would be a good thing again give examples of how others have done that and we're glad afterward we're glad we have done that to have reached out yeah for sure well definitely also be including some resources and links after in the comment section for those who are seeking resources but I also wanted to know do you have any recommendations of reliable sources for people to seek out to learn more or to get help yeah well it depends where what lives in many jurisdictions there are access points or some even official government you know website they say you know if you're in crisis call 811 or there may be a crisis line or there may be a crisis line a crisis team to to help out where the emergency rooms may be reach out to a family physician walking clinics any of that any of that you know it's often as simple as you know googling I live in such city services for depression suicide prevention anything anything and that can lead to the organized healthcare system and in some places quite well organized depending on the city and the jurisdiction so that's that's the first you know first thing to do logistically it could be quite difficult for minors like to kind of reach out right without parental permission and under very difficult circumstances where their parents might not be supportive or validating their feelings of depression what kind of well yeah that's what that's when that's that's cool that when at school often they are there may be a psychologist nurse or just a services school tell the teacher in many places there's been a lot of sensitization and information about mental health and mental health problem tell a teacher tell a friend and who who may be able to to help so that will be you know the way to do it of course you know walking into an emergency room you know that's possible it's not often that feasible for a young person so it's basically teacher friends if parents are not sensitive enough to understand or may not quite know what to do reach out at school that's that's it's often often a first good way of accessing help yeah thank you I think this leads in quite well to the idea of using the resources you can whether that's online or your friends your family to promote wellness so I do want to shift this conversation to questions that we've received from the community and then eventually the intrinsic practice on what one can do to really promote that experience of happiness and so the first question that we received is that what apart from things like you mentioned CBT medications what are some complementary medicine techniques for treating or maintaining wellness yes and so complementary medicine they are some like a mind-body approaches but there's also some pharmacological agents so for example there are some herbal compounds that like hypericum that may be useful that they tend to be useful in mild to moderate depression a mind-body practices can help especially when it's a complementary treatment or when we don't feel so good but it's not so so intense so we talk about even yoga chigong tai chi some acupuncture has been shown to have efficacy and depression was studied it was studied so all of these approaches can be useful but it comes to a point that even if these approaches are used and especially if depression is more than mild but moderate to severe then the medication combination with techniques like such as cognitive behavior therapy or interpersonal therapy should be considered we did some studies for example with the use of mindfulness right in different conditions it can help but typically it's not as effective as cognitive behavior therapy for example so it can be helpful but not would not be a first-line treatment other things that are important is what we call behavioral activation simple things such as trying to get up in the morning walk do a bit of exercise especially early in the morning so for some people a little bit of running can be good for mood and can can help I know it takes a lot of effort but these simple activities especially early in the morning tends to activate and help in re-synchronizing the day-night function because during a depression it can be a desynchronization of when we feel like falling asleep and when we get up and so it there is a desynchronization with the natural rhythm of day and night so having a bit of activity in the morning some some exercise can help to re-synchronize and eventually get back into a better rhythm and also better mood yeah so I think the key point just really to stay active even when it becomes quite difficult because I know a cardinal or common symptom of depression is like anodonia right so there's less will it let there's less pleasure like day-to-day activities and so it becomes really hard and then it kind of I think is a re-synchronizing cycle almost if they don't want to go out or walk take a walk or do simple things and then it kind of perpetuates that that cycle just you know yeah and so on that topic of promoting wellness a person Eliana from discord has asked about how can you kind of boost one's self-esteem self-confidence self-worth to maintain wellness yes so that's a very good question and it's part of self-knowledge and in a sense self-work so what does self-knowledge mean but self-knowledge means knowing our self and the way our body functions our body sensations it involves also knowing what emotions are the difference between negative and positive emotions and how to cultivate more the positive emotions and let go of the negative ones it involves knowing how to think how to think logically how to think in a balanced way optimistically with perspective so it involves doing more things rather than avoiding and isolating and then they are also what we call self-concepts so what is the self-concept self-concept is like a hypothesis or an idea about ourselves about how good we may be about how bad we may be about how complete incomplete so it could be you know i'm not worth of affection i'm not worthy of love i'm inferior i'm incomplete i don't have security so these are what we call notions or self-concept and through some work these can be understood because often they are like programs that work automatically in the background being unconscious but can determine our experience of life in relationships in what we do and the way we we see the world and see ourselves and it can be quite quite quite diminishing or inhibitory and can lead to depression or to nervousness so understanding ourselves at all these levels and understanding the self-concept self-hypothesis we can then modify them we can modify them to some affirmation to acting differently in situations to questioning ourselves and adopting a better self-concept it is doable so that's part of a therapy also yeah i really like the idea of making a hypothesis of oneself preferably to test whether you know to affirm one's hopefully self-esteem and improve that aspect yeah and some simple tools maybe also starting with sentences you know i um or i am not right so you so it could be i am worthy you know or i am unworthy or i will feel love if i do this right so that that starts to with the simple sentence we start to see how we really operate and whether we may see ourselves lower than what we are because very simply you know all of us human beings at birth we are a full human being in a sense we're complete and we we have all the potential to be a full well functioning and happy human being so we are all equal on that sense however we may not learn to recognize who we are recognize our what we call assets our qualities our talents and everything we may not learn because parents may not show us or we don't learn right so we don't often do not see how we use our potential and develop develop some ideas of ourselves which is lower than what we are right so i'm not intelligent or i'm not good enough i'm incomplete something's missing i'm an aberration that these are some of the self-concepts that can can be enough and unconsciously operational and lead our lives so these when we understand them and we see them then we can start to formulate other concepts and live by them it's not easy it's not simple it means some effort at first and determination but there are tools for that and the whole one of the goals of the intrinsic practice is to provide tools that can be tried on one's own to modify you know self-concept emotions stuff and so on so forth yes that is amazing i do want to highlight for all our viewers that just joined in the toolkit cycle the toolkit the intrinsic practice of psychological wellness program literacy program toolkit where one can explore the page to enhance one's ability to experience happiness and the links are in the description box below of the live stream so please take a look after we'll also get a few moments to chat about it after we answer some of the questions that we just got in from the live stream so these questions are first is from justine adam who asked is mental health openly talked about among young people in canada i know in other countries like japan india and indonesia it may be more stigmatized yes yes it actually depends on the on the country and it depends on also the the culture the culture and how it has evolved in terms of openness and knowledge on on mental health in canada for example there's more and more knowledge about mental health mental health issues depression anxiety and others there is more and more also self-disclosure of people who are well-known artists and even politicians and their experiences through problems such as depression there are also some youth organizations peer-to-peer support there are some groups like youth net which are really suicide intervention and help buy young people who who do peer support sensitization and more and more acceptance that you know depression is a problem it's a human problem that is important like any other problem may be important so there is less and less stigma but it's true it is true that it varies in one culture to another recently i've done work in in china in Shanghai and we see there that the government makes mental health problems as an important problem so it's part of the five-year plan so there's more and more sensitization to the need to have support and intervene and have also good primary care systems to address some of the mental health needs in that country in that culture so more most countries are going more and more towards openness and less stigma less of a negative perception of mental illness mental health problems so it's it's getting it's getting there but it's important to do more activities like we do to make it simple and make it acceptable and you know the way with the stigma thank you for the answering that question we've actually just got a bunch in right now so we'll keep the the rest pretty brief but hopefully comprehensive jazz scorpi has asked so do you recommend to kind of force yourself to do activities even when you don't want to in a depressive episode well forcing is a big word because you know it's hard to do activities and we're depressed but starting to do a bit more a bit more every day understanding that some activities moving something every day going out even walking connecting so that's called you know some behavioral activation yes will be useful but it's more important to do it stepwise in a gentle fashion then just you know pushing and pushing and pushing because that would put too much stress but you know planning in the morning I do a bit of five minutes of stretching I try to go out I try to walk I try to walk I try to connect with gently and add more and more and more yes because you want to activate it's also good for the brain to be to be activated the body but also connecting right so two activities going out speaking to people seeing people walking around for example that is that can be helpful so understanding that it will be helpful and add a bit more every day or every week and do more awesome so one final question from the community um live chat that is uh is from Ahmed who has asked that they stopped their medication and they're starting to get some side effect so why is it that their medication stopped working after it worked in the original um and why did it get better after they stopped medication even though they should have stayed depressed that is their question yeah so uh it's hard to answer a question just uh globally like this but medication uh uh can be very useful it has to be well uh tailored and well adjusted and uh sometime now there are are it has to be the right fit also that's why there are many medications and then you know being systematic about using them is important uh but if it's medication for a one episode of depression right usually it's recommended to take medication once one is well for about nine months to one year if it's for recurrent episodes of depression meaning somebody has experience one two three episodes then medication may be needed uh on the long uh on the long run so so then it's a question of uh you know choosing the the good the right medication at the right dose and uh adjusting it according to tolerance or side effects maybe shifting to another one if it's not the uh the good balance between the good effect and the side effects other rules that quite often is good to start low go slow I mean low dose but know that there's going to be a dose range to reach to feel to have more chance to feel well to the medication to its maximum effect any decrease of medication even if antidepressants are not medication that you get a huge withdrawal from when the when considering stopping medication let's say after nine months a year always do it very slowly very gradually so even every two weeks decreasing the dose a bit and even if it's done over a few months slower is better to decrease medications antidepressants thank you for answering the questions that were sent in from the live chat and thank you so much for answer for asking those questions with that I really wanted to finally shift to our last part of the live stream focusing on the value that the intrinsic practice can bring to enhance your experience of happiness so just as a recap for those that just joined us we talked about questions regarding depression in general more specific experiences of depression within oneself what you can do to help others then we talked about questions that were sent in to the live chat as this stream was happening I just also wanted to remind everyone that this will be available after our stream so you can watch it at any time at your convenience and with that let's talk a little bit about the intrinsic practice which viewers can find linked in the description box below be sure to visit the intrinsic practice calm follow them on linkedin instagram all links are below so would you like to tell us about the intrinsic practice and some of the steps that one can take to start this program and what can they expect this with pleasure so the intrinsic practice is an online program that is three with public service type of program three freely accessible it's basically a program or like a course to feel well to be well and to feel better in terms of one's mental health it is not a treatment it's not a treatment so it's not a treatment for depression but originally the intent to develop it was to help people who have gone through a depression felt better in a sense they had no more of the symptoms but wanted wanted to think more about not treatment but wellness and maintenance of wellness so we thought you know let's now give up the medical model which treats illness and symptoms and let's get more into a wellness model so and develop tools to help a person who was depressed or an anxiety problem and taking medication medication therapy and so now I want to think about wellness so this is a good program to want to enhance wellness now during depression it could also be useful with one's physician or therapist to consider accessing some of the tools because the tools that are in the intrinsic practice are derived from psychology neuroscience psychiatry such as cognitive tools or emotional tools and so on so they can also be used as tools in themselves in the context of a toolkit but otherwise if one is interested in just a wellness program or psychological literacy program so it's a program online as I said free that has been organized around six steps to get better to get to to get enhance one's experience of wellness or of happiness it is a like a course with homework and with tools that can can be used in the templates but it's around six steps so the first step is how to have a wellness practice for oneself how to do that the second one is how to define what happiness be for oneself because if one wants to be able to be happier better in life is to have a notion of what do they think happiness is that's not going to be my definition or your definition that can be good for everybody so that's step number two number three is about self-knowledge like we said earlier self-knowledge at the body level the emotions the thoughts the concepts and so on seven dimensions to know oneself better step four is knowing the world we live in in a sense that can be useful to understanding how the world can contribute to happiness step five is how to envision a happy life a very concretely situations the situation and step six is from our envisioning of how we would like to be in certain situations have specific techniques for could be thought techniques emotion techniques visualization it could be affirmations and so on so forth how to get there and be better and better and better in one's experience of life thank you so much for sharing the intrinsic practice with us all this is a self-paced accessible course right so anyone can access it whenever they want and however they'd like essentially that's right that's right so you go on the site it's free don't even have to register so this is totally confidential and you follow follow the various steps you know various steps with the lessons so it's reading and it's often a page is not that long so a few minutes to read there are many videos that give explanations and demonstration how to use the tool and they're all less than five minutes and homework to do homework to do because it's like a course in anything you want to learn music or learn the sports go to the classes it can be useful but a lot of it has to do with practice and homework and and repetition so but so what we find interesting and we're happy about is that it's been there with free access people who go on it more than once there's a good 30 to 35 percent of people who go back to the site from 25 to 200 times so we presume that they find it useful that's why they go go back to it and age ranges of access to the site are 18 to 24 24 to 34 in a majority so young people find it I guess they find it useful because they go back to it frequently that's amazing perhaps we can do some sort of session on discord which is discord.gg slash like to go where we can kind of answer questions that people might have about each step and we can discuss this further to see how one can really integrate IP into their day to day life. Yes yes and with concrete examples for example of how to use the tools and specific experiences yeah that would be a good to do yeah fun to do yeah. I've left the link to the intrinsic practice it's the intrinsic practice.com but I left the link at the description box the instagram the linked in also in the live chat box so if anyone would like they can definitely visit there also make sure to stay well and thank you so much Dr Bradwin for joining me today to answer these questions that the community has sent about depression. Well thank you Monica thank you psych to go and thank you all of you who have been at this session that it's very grateful thank you very much and good luck. Thank you so much. Yes thank you to Cindy thank you to the whole psych to go team and of course thank you to our viewers for joining us today together we can all make psychiatry accessible to all so have a nice day and make sure to visit the intrinsic practice and all the links in the description box below.


I'm Zor. Welcome to Unisore Education. This is the second part of lecture about decimals and relationship between decimal fractions and rational numbers. In the first part, I have proved that every finite or infinite periodic decimal fraction is a representation of a rational number. For instance, the periodic will be something like 0.142857 in a period, which means infinite number of times repeated, and this is actually one-seventh. Now, in this second part, I will try to prove the converse theorem that every rational number can be represented as a finite or infinite periodic decimal fraction. First of all, a couple of purely philosophical observations. Why am I proving this type of thing? I mean, this is definitely proved by many different people in many different ways, so the purpose of this proof is not really to prove. It's already proven. It's purely educational. More than that, I was trying to put together a proof which does not really depend on any kind of prior knowledge, any kind of a theorem which was proven by somebody else. It's a very, I would say, homegrown proof which anybody can do it himself, and that's why I think it's very important to really not to pay attention to whatever has been proven, but the way of the proof itself, because it might actually present certain logical benefits for you, and basically, again, the purpose is purely educational. That's number one. Number two, I would like to remind one very important piece of the previous lecture where I was talking about infinite geometrical progression. I will do it slightly more generally than in that lecture. If I have a sum of this type of members, so every next member of this progression is the previous multiplied by Q. Now, this is called the geometrical progression, and if Q is less than one, let's talk about the positive numbers only. Then, obviously, it's decreasing. Every member is smaller than the previous one by a factor of Q. Now, in this case, the sum of this infinite geometrical progression can be calculated very easily. I did it in the previous lecture in a slightly less general case, but anyway, the way how it is done is the following. I multiply by Q, all members of this thing. So, A times Q is AQ. AQ times Q would be AQ square, AQ, Q, etc. By the way, I do not remember the final formula. I always do this type of derivation and come with the formula, and that's basically something which I think is a better way. Well, unless you have an infinite memory, I don't know. It's easier to remember the way how the formula is derived than the formula itself, which might be quite complex. In this particular case, what I did was I multiplied by Q this sum, which means every particular member is multiplied by Q. As you see, this sum and this sum are very close to each other. You see, the difference is actually only A. Everything else is repeated, and this goes to infinity. So, the whole tale will actually disappear if I will subtract from one another. From S, I subtract SQ with the S minus SQ, and here, all these members will give the zero result. So, basically, that's the final equation which I have, which I can solve for S. S, obviously, is equal to A, A divided by 1 minus Q. This is the formula for a sum of infinite geometrical progression with the first member, A, and the factor Q, or multiplier Q, whatever you call it. Let's just remember it. I'll put it aside here because we will use it in the previous lecture. I also use this formula because if I have a geometrical progression, sorry, if I have a decimal fraction, periodic decimal fraction, actually it is the geometrical progression summed up because what this actually means is, well, let's illustrate it in a slightly more in a shorter example. Let's say you have 1 over 33, which is 0.03 in a period. Now, what is this? It means it's 0.03, 0.03, 0.03, etc. up to infinity, right? Now, these are periods which are repeated, infinite number of times. Now, the weight of this is 1 tenths, and the weight of this is 1 congrats. So, altogether, it represents 3 congrats. Or, if you wish, I'd rather say it's 3 to the power of 10 minus 2. Now, next 0.03, obviously, is what? It's 3 times 10 to the minus 4. Next 0.03 is 3 times 10 to the minus 6, etc. And altogether, it's basically, as some of these numbers, this, this, this, and all others. So, it's basically, it's 3 times 10 to the minus 2 plus 3 10 times minus 4 plus 3 10 minus 6, etc. etc. equals the first member, which is 3 10 minus 2 divided by 1 minus, and what's my multiplier? Obviously, it's 10 minus 2, right? So, that's what it is, which is equal to 3 hundredths, 10 minus 2 is 100, 1 minus 100 equals to 3 over 99, as I was saying, 1 third to 3rd. So, there is a very close relationship between infinite periodical decimal fraction and sum of the geometrical progression. So, this was used when I was proving to the first part that any periodic decimal fraction is actual irrational number, because this is actual rational number under any circumstances. And now, I will use the same concept of infinite geometrical progression to prove the converse theorem that every rational number can be represented by either periodic or final or periodic decimal fraction. Okay. Now, before proving this, I will simplify my task. If I have a rational number m over m, if I will prove that 1 over m is a periodic decimal number, then how can I say that m over m is also periodic? Well, it's based on something which I presented as a problem one for this particular theme of rational numbers. Problem one is prove that sum of two periodic decimal fractions is periodic. I would like you to think about this as a very simple problem. And I will also make a small presentation about how to solve this problem, but I really don't want to talk about this right now because it kind of diverts us from the main goal. But I hope that intuitively you feel that if you have one periodic decimal number and another periodic decimal number, then their sum will also be periodic. It's important for this particular theorem. And so instead of proving for any m over m, I will prove only for 1 over m, because if I will do this, then I will add my periodic number which is the result of this to itself a couple of times. For instance, how about 2 7s? Well, 2 7s is 1 7 plus 1 7, so I add these two together. Now, this is periodic and that is periodic, and the sum will be periodic as well. That's the problem one, try to do it yourself, and I have, I will present my own decision as well. Okay, so I will concentrate only on 1 over m type of rational numbers, but even that I will try to simplify a little bit more. And here is what I'm going to do. I would like to say that instead of proving for any m over 1 over m, I will prove this theorem only for those m which are not multiples of 2 or 5. And let me explain why. For instance, n is a multiply of, let's say, 2. It's 2 times k. Then I can always write that 1 over n is equal to 1 over 2 times k, or it's 5 over 10 times k. Okay, to prove the periodicity of this decimal representation, it's enough actually to prove the periodicity of this, because this is, it's basically the same thing as I started. Instead of proving for m over n, I can prove for 1 over n and then add it up. Same thing here. I can prove the periodicity of the decimal representation of this and add it to itself 5 times. Now, how about periodicity of 1 over 10k? Well, here it is. If 1 over k is periodic, let's say 0. Well, let's just use this example. 1 4 2 8 5 7. In this case, k is equal to 7. So 1 over k is this. Now, what is 1 over 10 times, which is 10 times smaller, very easily. It's 0.0, 1 4 2 8 5 7. Every decimal digit, I shift it to the right. Since the weight of this was, let's say, 1 tenths, shift it to the right with 1 over 100, which is 10 times smaller. Same thing with this one. 4 used to have a weight of 1 over 100. Now it's 1 over 1000, 10 times smaller. So every number, when I shift the whole set of digits to the right and put 0 in front of it, it's actually divided by 10. So division by 10 in the denominator of this rational number does not really change the periodicity. So instead of proving the periodicity of this, I can always prove the periodicity of this. So it's very important that from the very beginning, I consider n those which are not multiples of 2 or 5, because these can be converted into 10 times something. By the way, similarly, if I have n equals to 5 times k, I can always say that 1 over n is equal to 1 over 5k, which is 2 10 over k. So instead of proving the periodicity of 1 over n, I can prove the periodicity of this. Instead of this, I can put 1 over 10 over k, and instead of 1 over 10 times k, I can prove 1 over k again. So any number n, which contains 2s or 5, can be actually reduced to whatever is the smallest number, which is not divisible by 2 or 5. For instance, instead of proving the theorem for let's say 1 over 35, I can say that 35 is divisible by 5. So it's actually 1 over 5 times 7, which is actually the same as 2 times 10 over 7. And if I prove the periodicity of 1 over 7, which is this one, it's sufficient to prove the periodicity of 1 over 35. Okay. So enough that we are considering the rational numbers 1 over n, or the more formal representation, as I used to use when I was defining rational numbers, it's this representation. And n is not multiple of 2 or 5. Okay. I just invented this sign, not multiple of. There's probably something else that doesn't really matter. So n is not multiple of 2 or 5, and therefore not multiple of 10, of course as well. And now the proof. Okay. I will use this 1 over 7 as an example, I think it would be easier. So in general, if I have 1 over n, I will consider n numbers 9, 999, 999, et cetera, up to 9999 n times. In my particular case of 1 over 7, I will consider 9, 999, 999. Okay. This is boring. 999, 999, 999, 999, 999. And one more, 7 numbers, from 9 to 7 times 9. These are just different numbers. Now, why could I choose them for very simple reason? You see this formula for geometrical progression? No matter what my period is, let's say in this particular case my period is, has the length of 6 decimal digits, then the next number will be this one multiplied by 10 to the minus 6 degree, because we're shifting everything to the right by 6 positions, which is 1 millionth, right? So the next 1, 4, 2, 8, 5, 7 will be 1 millionth of this one. The next one will be 1 millionth of that one, et cetera. So always my next member will be 1 over 10 to the sum degree to the power of 6 or 7 or whatever it is, smaller than the previous one. So Q for these geometrical progressions is always 10 to the minus something, like minus 8, I will put it. So for this particular case, it's 10 to the minus 6, because every new period is 1 millionth of the previous, because it's 6 positions to the right. So if Q is 10 to the minus something, then obviously 1 minus Q would be, for instance, 1 minus 1 millionth. What is this? It's 9, 9, 9, 9, 9, 9, 9 over millionth, right? So these are, that's why my 9, 9, 9s are come into play. Obviously I took it from proof of the direct theorem that every periodic rational number is rational. And now I'm just trying to reverse the logic, basically, trying to prove that every rational number is periodic. Okay, so I took these n different numbers, 9, 9, 9, et cetera. Now there are two cases. Either I will find among them a number which is divisible by n, or I will not. So let's just consider these two cases. Let's take the case number one. So there is some 9, 9, 9, 9, whatever, 9, 9, whatever, which is divisible by n, which is equal to n times k, let's say. Now what is this 9, 9, 9, 9, 9? Well it's 10 to some degree a minus 1, correct? Obviously. Every number which is represented as certain number of nines, well a number of nines in this case can be represented as 10 to the power of a, the a's power minus 1. Because 10 to the a's power is 1 and a 0's. So now we subtract 1, we have 9 nines, the a nines. All right, so having said that, I can say that n is equal to 10 to the a minus 1 divided by k. And we are considering this in a general case, so I will put it here, n to the a minus 1 divided by k. Now what will be in our particular case of 1 over 7? Well I made an observation that 6 nines is divisible by 7. 6 nines is divisible by 7 and it's equal to 1 over 2, 8, 5, 7. You see? This is the same number. So I've noticed that we are considering the case when one of these numbers is divisible by 7, right? So I indeed found one. So this is exactly the case when you have this particular number. When there is none, it will be another case. But right now we have found something which is divisible. And therefore I can say that 10 to the minus 10 to the 6 degree minus 1 divided by k which is 1, 4, 2, 8, 5, 7 is equal to 7. This is exactly the same in our particular case. Okay. Now what can we do about this? In a general case we can say that 1 n, 1 over n is equal to k divided by 10 to the a minus 1 which is equal to k times 10 to the minus a and 1 minus 10 to the minus a. I multiply by 10 to the power of minus a, numerator and denominator. So this will be in the numerator obviously. And the denominator, if I multiply 10 to the a times 10 to the minus a, I will have 1. And if I will have 1 multiplied by 10 minus a, it will be 10 minus a. Now this obviously is exactly like this formula. Now in our particular case, well that will be 1 7 equals to 1, 4, 2, 8, 5, 7 times 10 to the minus 6 divided by 1 minus 10 to the minus 6. Well that's it. The theorem is basically proven. Because as you see, since this is exactly this, I can say that k times 10 to the minus a, k times 10 to the minus a is the beginning. That's the first member of my geometrical progression. And 10 to the minus a is its multiplier. So next one will be k times 10 to the minus 2a plus k times 10 to the minus 3a, etc. Which express is a decimal number, k is some integer, right? So k times 10 to the minus a will be something like 0 point and some digits here. How many digits? Eight digits, right? Then I have the same k shifted to the right by again taking eight digits. So it will be the same digits which are here, will be the same on the second group of eight digits. And then another eight digits, etc., etc., after infinity. In our particular case, what will be is k times 10 to the minus a, which is this, is 0 point 1, 4, 2, 8, 5, 7. Next one will be shifted by one millionth to the right, which is 0 point 0, 0, 0, 0, 0, 1, 4, 2, 8, 5, 7. Next will be 0 point 0, 0, 0, 0, 0, 3, 6. And then again, 1, 4, 2, 8, 5, 7. And when we summarize them all together, it will be 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7 because the rest are zeros, etc., etc., etc., which basically forms the periodic decimal number. So we have proven the theorem for a case, except one small detail, but I don't want right now to talk about this small detail. You can probably read about this in the written part of this lecture. It's really about the size of k. So the k to the 10 minus a is within the eight digits, no more than that. So it doesn't overflow the period. But that's minor point and you can read about this yourself. So anyway, we have proven the first case when 1 over n is a rational number and then we consider n numbers 9, 99, 999, etc., up to 999 n times. We have assumed that there is one of these which is divisible by n. What if there is none? Well, that's actually quite easy to deal with. You see, these are n different numbers. If you divide by n, n different numbers, how many different remainders you can get? Well, if you divide by a number and it's not divisible, then you can have a remainder 1 or 2 or 3, etc., or n minus 1. So different remainders are from 1 to n minus 1 when you divide something by n. These are your remainders, 1, 2, 3, etc., n minus 1. There is no remainder n because it means it's divisible. And then n plus 1 remainder is actually the same as 1. So obviously, there are only n minus 1 remainders which can be obtained if you divide all these n different numbers, which means what? That some of these numbers, at least two, have exactly the same remainder. Remember this famous principle of Dirichlet, if I'm not mistaken. If you have 101 rabbits and only one cages, you cannot place them in each individual cage. At least couple of rabbits should be in the same cage. So here is the same. We have n numbers but only n minus 1 different remainders. So at least two of them must be the same. So let's consider that you have two different remainders which are the same. And let me exemplify it again with some numerical example. I will use example 1 over 70. I know this is not exactly what I was considering in the beginning that the number n does not have divisors of 2 nor 5. And this does have it. But I needed just to exemplify about remainders this thing. So considering this principle I have to take 70 different numbers, 9, 99, 999, etc., up to 79 in a row as a big, big, big number. Now, if I will start dividing it by 70, I will start getting certain remainders. But 9 gives a remainder 9 if you divide it by 70.  Don't ask me how I know about it. Actually, it's very simple. If 6 nines is divisible by 7, then 6 nines and 0 is divisible by 70. So 9 extra and that's that's why 9 is a remainder. So these two numbers represent numbers which have the same remainder when divided by 70. So if two numbers have the same remainder, then their difference is obviously divisible by the number. So this minus this is divisible by 70, which is what, 999, 999, 990. In the general case, I can also say that something like 999, 999, 990, and then 0, 0, something 0, you have, let's say, K9s and L0s. Would be if I subtract these two numbers, which have the same remainder. So one number would be 999, 999, all of them, and another would be 999, the smaller one. So if I subtract, I will have number of 9s and number of 0s. Same thing here. Now, so my statement right now is that if there is none which is divisible by n, then there is definitely a pair which has the same remainder, and their difference looks like this. OK, so this number is divisible by n. So we can say that this number is equal to n times K. OK, what's the result of this? Well, obviously, we can say the following. This number represents something like 10 to the power of m minus 1. That's the 999, 999 minus a smaller 999. 10 to the power of, let's say, I probably have to use different letters here. I'll use lowercase m and n minus 1. That's what this number is. All 999s will do this, and smaller 999 will do this, which is obviously equal to 10 to the m minus 10 to the n or 10 to some number, well, let's say n is smaller than n. And you can have that m times 10 to the m minus n minus 1. And this is equal to still the same thing. Now, I shouldn't do it good. Yeah, we can do the n times K. Now, here is what's important in this particular case. Let me just leave the very last formula. We have, from the very beginning, assumed that n is not divisible by neither 2 nor 5. What does it mean? It means that this 10 to the n degree has no common multipliers, no common divisors, with n, because this has only 2s and 5s, which means what? That this number should contain all the prime numbers which comprise the number n. So no matter what number n is, if you will represent it as the product of certain prime numbers, let's say, then all these prime numbers should be here. None of them is here, because there are no 2s and no 5s, which means that 10 to the n minus n minus 1 is actually divisible by n times some number l. So my initial suggestion that n has no divisors of 2 or 5 actually means that this, my initial suggestion of the case 2, that there are no numbers among these n, which are divisible by n, really cannot be true. If I assume that this is a true statement, that there are two numbers in this group, which give the same remainder, then I will come up with this formula. And from this formula, what follows is that since 10 to the n degree has nothing to do with n, then this number should be divisible by n. And this number is definitely among these. So there is no such case when the number n, which is not a multiple of 2 or 5, has no divisors, has no numbers among these which are divisible by n. So this situation is just impossible. Case 2, when there is no number among these, which is a multiple of n, it's not possible at all. So that basically ends up the case 2. And everything goes back to the case 1. And the case 1, we have already proved. That proves that every rational number can be represented as a finite or infinite decimal periodic fraction. Well, that's it. Now, we still have the problem number 1, which is about summing of two different periodic numbers. You have to prove that this is also a periodic. And I would definitely suggest you to do it yourself. It's not a difficult thing. But anyway, I will provide a small lecture about this particular problem. OK, that's it for today. I hope you enjoyed it. Thank you very much.