It is now time for oral questions. I recognize the leader of His Majesty's Loyal Opposition. Thank you, Speaker. This question is for the Premier. Speaker, I think I speak for all of us here when I say that our thoughts, again, are with the people and communities that are directly impacted by the forest fires that are blazing across this province, and with also, of course, the courageous firefighters, pilots and local teams working to get them under control. And while that work is underway, millions of people across Ontario are experiencing the impacts to air quality. Speaker, we are in for probably the most severe fire season our province has ever experienced, and people are quite rightly worried for their immediate future and whether this is the new reality. Does the Premier acknowledge that the climate emergency is making this fire season significantly worse? Well, I want to thank the Leader of the Opposition for the question. Mr. Speaker, I want to start off by thanking all the firefighters and crews working around the clock to keep our communities safe. And Mr. Speaker, they're literally the best in the world, and again, I want them to know that I'm sure all of us, of all political stripes, have their backs 100%. I know that many towns and cities across our province are being impacted by smoke, and not just Ontario, but other smoke coming from other provinces where we're seeing this right across the country, unfortunately. This is having a major impact on many residents in these areas, particularly in Ottawa area and Northern Ontario. And it's hurting those who are already at risk, like our young people and our seniors. While it's taking place right now, I want them to know that our own fire ranger crews, helicopters, water bombers are responding in full force to manage the files. Thank you. A supplementary question. Thank you, Speaker. I appreciate that. I will point out that my question was whether the Premier would acknowledge that the climate emergency is making the fire season worse. And I, Speaker, yesterday, the Minister of Natural Resources and Forestry refused to acknowledge a connection between the climate crisis and these forest fires. All while this government is doubling down on costly and carbon-intensive gas-fired power, they're doubling down on sprawl, they've failed to deliver badly needed transit. Order. And the Conservatives also, let's not forget, weakened their own climate targets, Speaker. I want to ask the Premier, will the Premier show some leadership today and act on the climate emergency? Premier? Well, Mr. Speaker, I'm actually in shock that the Leader of Opposition is politicizing wildfires. It's staggering, really. But nothing surprised me with the opposition. We're taking steps to make sure we're prepared since 2017, with increased spending on emergency fire preparedness by more than 37%, Mr. Speaker. We have 142 fire ranger crews, which are the best in the world, ready to go right across our province, and we have a fleet of 28 aircraft to fight these fires, including nine heavy water bombers. My number one goal is to make sure the communities and the people are safe here in Ontario. We will spare no expense to make sure that we support our firefighters and our communities. And our supplementary? It's science, right? This is no ordinary fire season. People are worried that this is our new normal, and they are scared. In the GTHJ last night, the Air Quality Index was among the worst worldwide. And in the Ottawa region, the index was above a level 10, which is about as high as it gets, while people closest to the fires are being evacuated, schoolchildren in our largest cities are being kept inside. And people with medical conditions are being told not to go out. This is not normal, Speaker. With the very real impacts of climate change being felt by millions of Ontarians today, will the Premier reverse course on his plans to pave over the province's largest carbon sink? The Green Belt. The question. Will the Premier take their seat? Members, will the Premier take order? Order. Premier, can reply? Yes. You want to politicize it, but let me tell you the report that I've heard, Mr. Speaker, the report that I have heard, approximately 50% of the fires are started by lightning strikes. The other 50% are people starting campfires, not putting out the campfires properly. So I'm asking every Ontarian, please do not light any campfires. We're out there, all the firefighters, I should say, fighting against these wild fires. And yes, Mr. Speaker, they happen every single year. Similar to the floods, the wildfires start every single year. We will throw every resource we can to make sure we put these fires out. Thank you. For the Opposition. For a little leadership here and maybe take a little responsibility. Order. Government side will come to order so that I can hear the member asking the question. We start the clock. Leader of the Opposition. As we all know now, insiders with connections to private health care companies have donated over $35,000 to the Conservatives since the 2018 election. Donations from private clinic owners, developers looking to build private hospitals, all while the Conservatives are funneling public money out of our public system and into private health facilities. Here to the Premier, will the government prioritise sick Ontarians over their insider friends looking to make a buck? Hi, the Deputy Premier, Minister of Health. What we will do is we will continue to prioritise in making sure that we eliminate and decrease the wait times. People do not want to answer the passage of Bill 60. That means individuals, a physician who practices in British Columbia can come to Ontario, cut through the red tape and begin serving their communities here in Ontario. How do we do that? We do that through state programs that as of yesterday had 4,000 nurses part of that program to ensure that as they get their tuition and education costs covered, they are prepared to serve in underserved communities. We're doing the work, we're making those commitments and absolutely Bill 60 will expand the surgical and diagnostic centres across Ontario. Why? Because people are sick and tired of the status quo and sick and tired of waiting for their service. No, that's a no then. Is it? Speaker, there are new reports about a growing number of registered private healthcare lobbyists with ties to the Conservative Party. More insiders, lobbying their friends and their former colleagues, case in point, a former staffer for the Premier is now lobbying for a, quote, publicly funded, privately delivered care. Only he registered as a lobbyist before this government announced they were starting to issue private surgical contracts. How convenient, Speaker, to the Premier. Were these insiders given a heads up about the expansion of private surgery delivery in Ontario? Minister of Health. The member opposite does know that there are over 600 independent surgical and diagnostic centres operating today in the province of Ontario, right? This is an expansion of a program that has for decades served the people of Ontario well because they don't want to have to go to a community an hour, two hours away to get their CT scan, to get their MRI, to get their cataract surgery. They want to have that opportunity in community. We are expanding a program that has served us well, but we need to make sure that we have capacity as Ontario grows, as our population increases, and frankly, the need for these services increases. Thank you, Speaker. The final supplementary. I don't buy it, I don't buy it for a second, Speaker, and neither do Ontarians. Because they know this government's track record of helping their friends at the expense of everybody else. Speaker, the Office of the Integrity Commissioner reports there are nearly 1,200 lobbyists registered to influence this government on health policy. That's more than on nearly every other issue combined. Many are lobbyists for profit, private healthcare companies who offer nearly identical services to those covered by OHIP. Only they let the richest pay out of pocket to cut the line and access services faster. They're swirling like vultures, vultures over what's left of our healthcare system, and they're looking to cash in Ontarians' health. I'm going to ask again, when will this government prioritise sick Ontarians over their insider friends looking to make a buck? And the Minister of Health. Speaker, I would ask the leader of the NDP to turn around and ask her caucus how many of those caucus members are lobbying me every week on I have constituents who are waiting for surgery. I have constituents who are waiting for cataracts. Will you do something as the government? And I can assure our members that we are and we do. In January, it was a great honour to be able to expand surgical diagnostic centres specifically for cataracts in Windsor, Kitchener, Waterloo and Ottawa. Cataract surgery in the province of Ontario have their wait time shortened. What does that mean? It means they get back to their families, they get back to their community, they get back to work. It is exactly what your members' lobby means for on a weekly basis and what the people of Ontario deserve. Thank you. Stop the clock, please. I stop the clock as our honoured guests have to prepare for a reception and some official photographs and they may have had an off already and they found me to leave the proceedings at this time. Congratulations and thank you again to Monsieur de Rosier and Miss Deller for your service to December. And the people of Ontario. We will restart the clock. The next question, the member for Nickelbelt. Thank you, Mr. Speaker. Question for the Premier. Last week, Health Coalition from all over the province brought 400,000 Ontario voices opposed to private health care to this legislature. Today, Brock University students are here to show the opposition to build 60, the government health privatisation agenda. People representing Minden, Monforest, Palmerston, Listerwell, Wingham, Seaford, Clinton, Gray-Bruce, Chelsea, the list goes on, are here asking the Premier to either reopen their ER or keep them open. We live in a democracy speaker. All those people are coming to Queen's Park because they are scared. They're anxious. They're worried. They want to be heard. I want the Premier to listen to that. Minister of Health. As the member opposite knows, Bill 60 had fulsome public hearings where individuals could come forward and share their concerns, questions and frankly, platitudes for Bill 60. I'm going to highlight a couple of things that came out of those committee hearings. I'm here to say that Bill 60 is a good start in eliminating Ontario's surgical backlog. We are pleased to see this government introduce significant changes to our system that will better serve Ontarians within a publicly funded system. Overall, this bill sets up a good framework to create a system of surgical care that is patient-centred and promotes patient choice. That comes from the President and CEO of CE Health. Thank you, Speaker. Thank you, Speaker. Back to the Premier. In my discussions with Brock University Student Union executives, they voiced serious apprehensions about your government's health care, privatisation direction, especially concerning accessibility. Reduced health care impacts are evident in Niagara. Your two urgent care centres confront diminishing access. When asked, 85% of Brock University students are concerned over Bill 60, a sentiment shared by 400,000 referendum Ontario voters. Health care in Niagara is bearing the staff crisis magnifying by Bill 124 and your privatisation agenda. Premier, when your government stops shrugging responsibility and commitment to enhancing health care and flexibility in Niagara through public investment. Minister of Health. I hope when you were speaking to those Brock students that you talked about the investments that we are making, increasing the number of student seats for both post-secondary and residency positions, this means that there are more opportunities for young people who wish to practice medicine in the province of Ontario have that opportunity as a result of our government's investment. And I hope you also highlighted the fact that in the region of Niagara we are investing and building with that hospital corporation a brand new hospital in the amount of $4.1 billion in our community. Thank you, Speaker. Order. Next question, the member for Brampton East. Thank you, Speaker. My question is to the Minister of Economic Development, Job Creation and Trade. With our government's policies, Ontario's reputation as a hub for cutting edge innovation continues to grow. With its robust manufacturing sector, it's crucial that our government attract investments to take advantage of this fact as it drives towards creating an end to end economy and ending our reliance on other jurisdictions for critical goods. Speaker, can the minister please highlight a recent investment that showcases the province's commitment to fostering innovation and simultaneously supporting our manufacturing industry? The Minister of Economic Development, Job Creation and Trade. Speaker, Ontario is now the innovation and manufacturing gateway to North America and that is the result of reducing the cost of doing business by $8 billion every year. Hydrogen optimized recently announced a $4.6 million investment in Owen Sound. They specialize in the production of green hydrogen through an exciting new manufacturing technology. This will replace fossil fuels in energy intensive industries like cement and fertilizer production. They're doing this cutting edge work while creating new jobs and acquiring state of the art equipment for Ontario. With a $500,000 investment from our government, Speaker, this is how we're supporting our innovation and manufacturing sectors. Thank you, Speaker, and thank you to the minister for his answer and the great work that he does bringing new jobs to our great province of Ontario. It's evident that investments like these happen when government creates the right conditions for businesses to thrive and now more than ever, Speaker, it's important that the innovation and economy works hand in hand with the manufacturing sector. Thank you, Speaker. With this recent announcement from Hydrogen Optimized, can the minister elaborate on why companies like them are increasingly looking to invest in Ontario and grow in Ontario? Thank you, Speaker. Yesterday, my ministry was called into estimates. Now I have to confess the last time I was in that committee room was for the liberal gas plant scandal where senior liberal officials actually went to prison. The being in that room reminded me of the state of Ontario under the previous government supported by the NDP. 300,000 manufacturing jobs were lost. Companies were fleeing Ontario. We all remember those very horrible years. While that all changed under Premier Ford. Ontario is now the world's leaders in EVs with an unprecedented $25 billion in new business. $3 billion in new life sciences, $100 billion in tech, over 660,000 new jobs created. Speaker, that's the difference when you put in a government that gets it done. Thank you, Speaker. My question is for the Premier. Members of my community are anxiously awaiting the completion and opening of the Finch West LRT line. The construction phase hasn't been easy. With massive traffic disruptions, vehicular and pedestrian accidents, property damage complaints, a collapsed underground garage of a high-rise condo, I daycare flooded with sewage displacing over 100 children for months and more. My community has been patient, but understandably frustrated. In light of all of the issues on the Eglinton LRT, what assurances can you provide? My community that the Finch West LRT will be completed on budget and on time at this year's end. Thank you, Mr Speaker, and I thank the member for his question. It's an important question because the Finch West LRT will give people in the northwest part of the City of Toronto what they've been waiting for for a long time, which is a transit system that will offer more choices to travel on their own schedule. Mr Speaker, the Finch West LRT will connect the new Finch West subway station on the Toronto-York Spadina subway extension to Humber College. We're talking about 11 kilometres of new dedicated LRT with 16 new surface stops, Mr Speaker, a below grade stop at Humber College North Campus and an underground interchange station at the TTC's Finch West subway station. Mr Speaker, this also includes a brand new maintenance and storage facility for light rail transit vehicles. Mr Speaker, this system will transform the community. Shovels went into the ground in 2018, Mr Speaker. The constructors are working diligently to deliver the system, and we look forward to having good news. Thank you. And a supplementary question from the member for Scarborough, Southwest. Thank you very much, Speaker. Back to the Premier. Residents in my community have contacted my office to express their frustration, their distress over the incessant overnight construction carried out by Metrolinx. The disruptive noise has become so unbearable that constituents are complaining that disruptive noise just imagines someone drilling in your backyard all night long for a whole year.  However, Metrolinx has informed that residents that they possess a permit allowing them to continue this overnight operations till the end of the year because it's related to the transit system. Whether it's the Eglinton LRT, the Scarborough RT, or the Lakeshore East Line, Scarborough residents are the ones always to suffer. Question. Speaker, while critical transit work is being done, what will this government do to protect local residents and mitigate the ongoing disruptions to their lives and their well-being? Thank you, Speaker. To respond, the members will please take their seats. Premier? I want to thank you for your question. Does the Scarborough residents know you voted against that subway line? Do the Scarborough residents know that you had no interest in delivering the first subway in the history of Scarborough? When I was at City Hall, we were fighting for the residents of Scarborough where you never even existed. You weren't up there cheering for Scarborough. You didn't vote against your party. You should have voted against your party. You know something I'll tell you? The reason why the majority of the seats in Scarborough is because they know we're getting things done. We're building a subway for the first time in the history of Scarborough. We're making sure they're getting a new hospital. We're getting a university. Premier, please take a seat. So a few reminders. A few reminders. A few reminders. We make our comments through the chair, not directly across the floor of the house. Secondly, once the speaker stands, you sit.  When I can't hear whoever's got the floor because of a loud ovation, we stop the clock because there's no point in carrying on. So we'll start the clock. Next question, the member for Scarborough Centre. Thank you, Mr. Speaker. My question is for the Associate Minister of Transportation. When it comes to community around the greater Golden Horseshoe, investment is critical. Transportation infrastructure needs to happen now. I'm fortunate to have the GO train station in my riding, but more GO rail service are needed across the region. Unfortunately, the previous Liberal government did not plan ahead to address the 40 transit need for people in Ontario. Our government must continue to take action and to do more to provide GO train expansion. Speaker, can the Associate Minister please explain how our government is expanding GO rail services? The Associate Minister. Speaker, I am very happy to keep talking about Scarborough and let's get to it because there's a lot happening in that member's riding. Let's talk about crews widening the Shepherd Avenue West Bridge between Bakersfield Street and Chesswood Drive for the increased future service that GO expansion is bringing to the very line. In fact, construction is well underway and is slated to continue until September this year with bridge installations set to begin shortly thereafter. This is another vital infrastructure upgrade for our government that we are delivering. Game changing transit, that includes GO expansion that will see riders benefit from more than 6,500 weekly trips on the GO network. When you break it down, Speaker, what this really means is that we're ensuring that more people can connect to local transit work, health care education and other critical services across the entire region. Speaker, the Premier said it best. The member's opposite did nothing to build transit in this province that includes the fine people of Scarborough. We're doing things differently. We're getting it done. Thank you, Mr. Speaker. And thank you to the Associate Minister for the update on this important project. This is encouraging news for many people across the GTA. Transit infrastructure expansion is vital to help growth in Ontario's economy so that goods can get to market and so that hardworking Ontarians can get to their jobs. Our government must continue to invest in expansion of the transit services. Mr. Speaker, can the Associate Minister please explain how our government is delivering on transit services for the people of Ontario? The Associate Minister of Transportation. I sure can expand, Mr. Speaker. That's exactly what I'm going to do because we've been making some terrific progress on building transit. We were re-elected a year ago. GO expansion milestones. They include a completion of major construction on the Davenport Diamond and terrific new upgrades at Bramley, Maple, Millikin, King City and Aurora GO stations. Our historic GTA transit project, Speaker, we've awarded multiple contracts for the game-changing Ontario line and we've tunneled well over half the Eglinton West extension more than a month ahead of schedule. Speaker, we're also modernizing transit fare systems by introducing credit and debit payment features on GO transit and agencies in the 905 with over one and a half million taps and counting. And, Speaker, let's not forget, after the Liberals canceled the Northlander, our government brought back with a $140 million purchase to buy three terrific new trains because we're bringing the Northlander back. Speaker, the opposition left a giant transit deficit in this province. We're filling that gap and we're building record transit in Greatville. A member for Waterloo. Thank you very much, Mr. Speaker. My question is to the Premier. A core mandate of the Ontario Lottery and Gaming Corporation is to generate revenue for the province. By this metric, the government's ongoing plan to privatize operation of Ontario's casinos is a failure. Even before all of the contracts have been awarded, folding one third of the contracts were renegotiated, resulting in an estimated loss of $3.3 billion to the province. These renegotiations were done voluntarily. There is no legal obligation for the province to do this, and they amount to a subsidy. These subsidies have been used in the construction of these private casinos. We are subsidizing the construction of casinos in the province of Ontario. Why is this government continuing down this path and losing billions of dollars that are needed for healthcare, education, housing, and yes, the environment? Please tell the people of this province why the finance minister is overseeing and condoning this conduct. Thank you, Mr. Speaker, and through you to the member opposite. Mr. Speaker, many in this room are students of history. And let's go back to when the modernization plan was put together in 2012. Does anyone remember who was in power at that time? It was the Liberals. Oh yeah, it was the Liberals. Does anyone remember who supported the Liberals? That's right, that's right, 2012. So they put this framework in place, Mr. Speaker. So think about this, Mr. Speaker. We have to clean up the, thank you, of the previous government. I have, Mr. Speaker, full confidence in the Ontario Lottery and Gaming Corporation. We have regular contact with them, Mr. Speaker. And they are good people there managing the taxpayers' money. And since, to date, modernization has resulted in about $2 billion in capital investment from the private sector. You know what that means, Mr. Speaker? Good jobs, bigger paychecks for the workers of Ontario. Supplementary question. Thank you. Does anybody remember when we had a government that put the people we're elected to serve ahead of private interests? The OLG, with the permission of the Finance Ministry, was not required to renegotiate these contracts. Then they didn't need our help either. In one case, a private casino operator with over $3 billion in assets and a net revenue of nearly $300 million annually was given a sweetheart deal to reduce their revenue sharing with the province by 25%. Apparently, this government is more concerned about the financial viability of casino corporations than the needed revenue for education, health, housing, and, yes, fighting forest fires. Was this renegotiation really intended as a gift to friends or is the government truly so out of touch with the needs of Ontarians that they prioritize casinos over housing? This is unethical behavior. I'm asking the Finance Minister simply to do his job. Mr. Fene. I'm going to take the high road, Mr. Speaker. And, you know, Mr. Speaker, she talks about a pattern. She talks about remembering. Does anyone remember the events of June 2nd, 2022, where the people spoke and delivered a bigger majority to this side of the house and the great middle over there? Mr. Speaker, you know, we have an obligation to the workers, to the people of this great province, then the jobs that they create and the private sector to put. We don't create the jobs. The private sector creates the jobs. And let me talk about my own writing, pickering. And you know what we have in pickering now? A new casino, the Pickering Casino, which has created literally hundreds and hundreds of new good paying jobs right next door to Ajax, right next door to Whitmore, and, yes, right next door to Scarborough. This is what this government is about. It's about creating the conditions so jobs and people can work in this province and support their families. Question, the member for Don Valley East. Mr. Speaker, my question today is for the Minister of Infrastructure. In 1969, the Premier of Ontario at the time, the Honourable John Robarts, spoke at the opening of the Ontario Science Centre and shared the following statement. I am confident that during the next 100 years it will have an impact on far more people than any other single centennial project. 100 years, and that's from a progressive Conservative Premier. How emblematic of this government's general approach to doing things that they are choosing to demolish it in less than half that time. First, they take apart health care. Then the green belt, then the science centre. There's clearly a theme here. Yesterday I was joined by Opsuin community members to reject the government's decision to demolish and relocate the science centre, a decision I want to remind everyone, made without any public consultation. My question, Mr. Speaker, is when will this government commit to genuine consultation with the public on the science centre before making community destroying decisions like this one? Minister of Infrastructure. Thank you very much, Mr. Speaker. And thank you very much to the member for the question. Mr. Speaker, we made a commitment. We've been fully transparent with the public that we will be building a brand new science centre with additional more former science centre lands are an opportunity for the province to continue discussions with the City of Toronto. There are opportunities for community amenities for housing and we will have those discussions with the City of Toronto. But Mr. Speaker, we are bringing Ontario Place back to life with a brand new science centre with more exhibition space. Very supplementary question. Thank you, Mr. Speaker. I'll address the folly of that argument in just a moment because this government claims it consults with stakeholders, purports to listen to the public, and if it did so, it would hear the following things. This afternoon, I will deliver petitions from well over 30,000 people all calling for a halt to the demolition of the science centre. Nearly 900 pages of people offering their opinion if this government would just pause and listen to them. Instead, as we just heard what we're hearing are a series of nonsensical justifications for this decision. For example, while this government argues that the new location will attract more visitors, the new centre will be 50% smaller in size, many Ontarians won't be able to afford visiting the new centre and are only able to visit the one we have now because it is centrally located. Not to mention, the current site is situated at the intersection of the Eglinton Crosshand in Ontario line, which will open up the science centre to even more of the public. And so to the Minister of Infrastructure again, given this public outcry and these arguments, will they reevaluate the decision to demolish the science centre? Minister of Infrastructure. Thank you very much, Mr Speaker. The new location at Ontario Place will also be connected by the Ontario line, which is a brand new subway line that our government is building to provide greater public access to Ontario Place and make sure that it's accessible to the public. Mr Speaker, we are building a brand new science centre, an innovative place with new exhibition and additional exhibition space. We are bringing Ontario Place back to life. We anticipate 4 to 6 million visitors a year, and we are all excited for the site servicing work to start, and we will continue working in a collaborative way with the City of Toronto. Thank you. The next question, the member for Brampton East. Thank you, Speaker. My question is to the great Minister of Labor, Immigration, Training and Skills Development. Our government believes that anyone who wants to work should have the opportunity to work. However, individuals with developmental disabilities often face barriers in securing stable and fulfilling employment. Speaker, the statistics are clear. There are approximately 2.6 million people in Ontario who live with disabilities. Sadly, only 55% of these people are employed. Individuals with disabilities deserve opportunities to master in-demand skills, gain valuable experiences and build the confidence they need to thrive in their communities. That's why our government must continue to make investments that would build up Ontario's workforce. Speaker, can the Minister explain how our government is supporting employment opportunities for all Ontarians? Mr. Labour, Immigration, Training and Skills Development. I just want to thank the member from Brampton East for this really important question. Speaker, giving people with disabilities a hand up to a better life isn't just the right thing to do. It's also good for the bottom line. We owe it to all of them to build an Ontario that truly leaves no one behind. That's why I was pleased to join everyone's favourite minister, the Minister for Seniors and Accessibility at Community Living Toronto. We were at Community Living Toronto to announce our government is investing six and a half million dollars to support five innovative training projects to help nearly 4,000 people with disabilities find meaningful employment. Under the leadership of our Premier, our government believes everyone deserves a fair shot at a purpose-driven life. Through these projects, participants will get tailored supports to learn new skills, set goals and be matched with mentors who can help them succeed. Thank you, Mr. Speaker, and I look forward to talking about these projects more. Thank you. Supplementary. Thank you, Speaker. Thank you to the Minister for that great answer. And Ontario continues to face a historic labour shortage with nearly 300,000 jobs going unfulfilled every day, costing our economy billions in productivity. While our government's investing in training programs and providing support, there must also be accessible and inclusive employment opportunities. And as the Minister states, we need all hands on deck in order to build a stronger Ontario for the next generation. That means we must ensure all Ontarians have access to the skills they need to find rewarding jobs. Speaker, can the Minister please explain how investments by our government will open pathways for more inclusive workplaces? Thank you, Speaker. Once again, the Minister of Labour. Thank you and thank you again for that question. Speaker, creating an accessible world requires a commitment from everyone. Since day one, our government has been working with workers, unions, industry associations and all of our other partners to help people get better jobs and bigger paychecks. We have been on a mission to help individuals with disabilities secure meaningful and rewarding careers with employers in their own communities. Through the projects we announced during National Accessibility Week, we're helping those who need us the most get started with paid job placements in in-demand sectors like healthcare, information technology and hospitality. By working with all of our partners and continued investment to help people with disabilities find careers, we are continuing our mission to make Ontario the best place to live, work and raise a family. Thank you. Next question, the member for Niagara Falls. Thank you, Mr. Speaker. My question is to the Premier. In Niagara, I met with unionized frontline workers from long-term care homes who are concerned about the use of agency employees and the effects on the quality of care for residents. Permanent employees in long-term care are not paid fair wages for their work, which often leads to them leaving the jobs they love, worsening the staffing crisis. Meanwhile, temporary employment agencies are charging $150 an hour or more in Ontario's footing the bill with a premier, Iranian temporary staffing agencies and ensure permanent employees are paid fairly to address the staffing crisis. That's good. That's good. Deputy Premier and Minister of Health. Well, the member opposite is going to disparage individuals who are regulated under the same regulated health profession as nurses working in hospitals, in long-term care homes. We are going to embark on and continue to expand upon the largest health human resource expansion in the Ontario's history. Now, last summer, when we directed the College of Nurses to quickly expedite review and ultimately license appropriate nurses that have been trained in other jurisdictions, they had a historic high in 2022 over 12,000 nurses, over 6,000 of which were educated outside of Ontario and Canada have now been given the opportunity to register and practice in the province of Ontario. Those types of initiatives are going to expand our health human resources so that everyone, whether they are in community, long-term care, hospital, in our surgical and diagnostic centres have appropriate care. Supplementary? Let's be back to my premier, but I will say to the health minister, 5,600 have died in long-term care facilities, so this is a really concern. Many of the temporary agency workers have no training or experience in long-term care. This is leading to reduced quality of care for residents and the potential concern around the safety and wellbeing of the people in our long-term care facilities. These are our mothers, our fathers, our grandparents, our aunts and our uncles. It's all about respect and dignity for long-term care residents and for the permanent employees in these homes. When is the premier going to share fair standards are in place at every long-term care home across the province of Ontario for workers and their patients? The House Leader, Minister of Long-Term Care. Mr. Speaker, the member knows that we did bring in North American leading standards with the Fixing Long-Term Care Act. The member also knows that he voted against that. The member should remember that we did increase wages for our PSWs. He will recall that he also voted against that. The member probably recalls that we also decided that we would hit a North American leading standard of four hours of care per day. He voted against that. Moreover, he voted against, I think, an additional $25 million for the long-term care homes in his own riding to increase the level of care in his own community. He's voted against the additional homes that we're building in his riding and across Niagara. Mr. Speaker, he's talked against the long-term care expansion that we are doing. He's talked against and voted against the inspections, the increase in inspections that we're doing in long-term care. By every single measure on care has the largest investment in long-term care in North American history. Not just in Canada, but in North America. And on every single time he had to support that, he and his party voted against. The next question. The member for Chatham Kent Leaning Chair. Mr. Speaker, my question is for the minister of colleges and universities. Under the leadership of our premier, this government has made record-setting investments in healthcare infrastructure, more support for healthcare workers, and unprecedented support to accessing care. Our government believes that everyone deserves to have access, equal access to healthcare, close to home. We know there's more that needs to be done when it comes to connecting Ontarioans to care in their local communities. This means that more staff are required to better serve our communities and the greatest need for healthcare is in professionals. However, filling these critical roles requires educated and skilled healthcare professionals. The minister had previously spoken about the Ontario Learn and Stay program, which incentivizes students to pursue careers in the healthcare sector. Speaker, can the minister please provide an update on the success of the Ontario Learn and Stay program? Good question. Mr. Colleges and Universities. Well, thank you, Mr. Speaker, and thank you to the great member for that question. And yes, I would love to provide an update on the Learn and Stay program, which I've had the opportunity to speak about this exciting grant on several occasions in the House and how it will directly address the healthcare challenges Ontario is facing. On May 16th at Georgian College in Owen Sound, alongside Minister Jones and MPP Byers, we announced the launch of applications for the new Ontario Learn and Stay grant. Incentivizing students to study and work in the sector will not only alleviate the healthcare strain and bring stability to underserved communities, but it will also steer students in the direction of meaningful careers. Speaker, I'm pleased to report that to date as of 9 a.m. this morning, we have had 4,135 students start or complete the application to the Learn and Stay program. Very good. That's great. This is how students are eager to begin lifelong careers in the healthcare sector. Unlike previous governments, this government is taking an all-hands-on-deck approach to supporting students in every way possible to support our workers. Thank you. Thank you very much. This supplementary question. Thank you, Speaker. It's so encouraging to hear the Ontario Learn and Stay grant program has been so well received by students looking to pursue meaningful careers in healthcare. We know that some regions in our province face urgent staffing shortages. This uptake in applications will greatly assist in filling these local healthcare staffing needs. While the Learn and Stay grant program is a positive step in addressing staffing shortages across Ontario, our government must continue to be proactive by implementing programs to produce results. People in communities like Chatham-Kent-Lemington and across the province are looking for assurance that when they need access to healthcare, the professionals will be there to care for them. Speaker, can the minister please provide an update on how local communities will benefit from students enrolled in programs through the Learn and Stay grant program? Minister of Colleges and Universities. Thank you again to the member for that question. And yes, I'd love to provide more specific details on this grant. In Northern Ontario for the member for Thunder Bay-Atacocan, 237 students have applied to programs at Lakehead University and Confederation College. These are students who will go on to work at Thunder Bay Regional Health Sciences Center and St. Joseph's Care Group and more within the region. In the east, the member from Renfrew-Nipissing Pembroke, 106 students are eager to attend programs offered at Algonquin College that will support healthcare needs for Pembroke Regional Hospital and Deep River District Hospital. In the southwest, the member for Windsor-Tacompses, 387 students healthcare needs across the entire region, including at the Windsor Regional Hospital. And Speaker, that is obviously only a handful of the writings represented and the number of applicants increases every day. When our premier promises to get it done for the people of Ontario, we get it done. The next question, the member for Parkdale High Park. Thank you, Speaker, my question is to the Minister of Education. The foreign conservative government is refusing to reimburse $61 million the TDSB was forced to spend from their reserves during the pandemic. The government knows that school boards cannot run deficits, which means TDSB is being forced to make cuts. Now across Toronto, schools are learning that staff positions will be cut. Teachers, education assistants, councillors, vice-principals, 522 staff positions cut. This government is starving the public education system. Speaker, we know conservatives don't like public healthcare. Are they now after a public education system too? Mr. Speaker, we have increased funding for school boards by 14% when compared to the former liberals. We have increased funding by $78 million for Toronto District School Board, even though it's the member opposite for whom we could disagree often on opinions, but not on facts. There's literally 8,000 fewer students and yet they have $70 million more than they did when we started. And as the member opposite will know, as a parent and a parliamentarian, the funding, the per-people funding, when student enrollment rises, funding rises. When enrollment declines, as does the funding. It's commensurate with the amount of kids in the system. Yet even with fewer kids, funding is up. And that's such an important point for people in Toronto to know. We are stepping up with investments in Toronto. We're building modern schools in Toronto. We're expediting the delivery of schools in the city of Toronto. We're building in all of your communities because we appreciate there's more to do. The best way we could help Toronto is vote for our budget, vote for our plan, vote for a responsible course of action that lifts standards, elevates the expectations of the system and stands up for tax. Thank you, Speaker. The only record here is how often the minister can repeat the same talking points while per-student funding is down $1,200. Our kids deserve the caring adults they need in classrooms and they also deserve safe, healthy learning environments. We know that clean air improves health, reduces absences, and results in better learning outcomes and test scores. Yet this government isn't bothering to monitor, report on, and improve indoor air quality in schools. For a government that talks a lot about accountability, they sure have problems showing it. Ontario Schools Safety is here today calling for action. Will the minister meet with them and will the government fund an expert air quality committee to oversee air quality in schools? Thank you. Members, please take their seats. Mr.ification. Mr. Speaker, we invested $665 million over the pandemic to raise ventilation standards in Ontario. Mr. Speaker, there are more HEPA filters. There are more HEPA filters in this province than in every province combined. 100,000. The member opposite has the gall to speak about transparency. We are the only jurisdiction in the nation that required every school, 4,800 schools, to publicly report on the state of ventilation at the school level, the rate of ventilation, the use of filtration. We require every school to have a MRF 13 for the schools that have mechanical ventilation. We have a standard that no province has. If a school does not have mechanical ventilation, we require a HEPA filter in every single learning space, the classes, the gyms, the libraries, the learning commons. That is the gold standard when it comes to elevating expectations of ventilation. And Mr. Speaker, if the member opposite was so concerned about this, then you should explain to the parents here why you voted against the measures that improved the air quality in Ontario's public health. Remind the members to make their comments through the chair, not directly across the house at each other. Start the clock. The next question, the member for Brantford Brands. Thank you, Speaker. My question is for the Associate Minister of Housing. For too many Ontarians, including young people, newcomers and seniors, finding the right home is still too challenging. The housing shortage is affecting all Ontarians, including rural, urban and suburban communities across our province, and it has unfortunately reached crisis levels. Our government has been working on behalf of the people of Ontario to address the shortage of housing in our province and has passed several pieces of legislation to significantly increase the supply of housing. However, our government must do more to find solutions to address the housing crisis and to speed up the pace of housing construction. Speaker, can the Associate Minister please explain how our government is removing barriers to getting more homes built in Ontario? Thank you. Associate Minister of Housing. Thank you, Speaker. And I really do want to thank the member from Brantford Brands for this great question. Speaker, we are undertaking thoughtful, impactful actions to address housing affordability and supply for all Ontarians. Our latest action plan allows our government to boost construction while supporting current and future homeowners and renters. It is this government that is protecting tenants from unfair practices. We're reducing red tape and we're assisting first-time buyers, something the NDP once again voted against. Speaker, we've laid the foundation to increase the supply of market housing so that affordability is within reach for every single community across this province. And Speaker, I've been to Ottawa, Perth County, Wellington and London, right across many communities and we've heard the same about the need and the appreciation for the bold measures our government is taking to combat the housing supply right across this province. Thank you. And a supplementary question. Thank you, Speaker, and thank you, Minister. Everyone in Ontario should be able to find housing that meets their family's needs. And while it is encouraging to hear about the progress our government is making to remove barriers to construction, I will say it again. There is much more that needs to be done to increase the housing supply all across Ontario. It is positive to see that several municipalities have committed to achieving our province's housing targets and their support is vital to accomplish this goal. The commitment by municipalities to work collaboratively with our government in developing strategies that will provide real and long-term housing solutions is important and essential. Speaker, can the Associate Minister please explain how our government is supporting municipalities across our province so they can deliver on their housing commitments? Thank you. And again, the Associate Minister has. Thank you, Speaker. And once again, thank you to the great member for the question, Speaker. Municipalities across Ontario getting on board, helping to deliver on their housing pledges and to increase supply. But, Speaker, once again, the opposition continues to vote against the best interests of the people across this province. Speaker, they acknowledged we were in a housing supply crisis, although they can't seem to agree if it's real or not. Order. But then voted against our latest housing supply action plan to get more housing supply built. They take to the streets with sign saying they support tenants' rights, Speaker. But then they voted no to the single largest renter protection legislation we've introduced so far, Speaker. It's our government that's reducing red tape. We're freezing costs. We're giving municipalities the tools needed to build the communities off tomorrow because we know the NDP that, once again, no development party are against getting anything done. Thank you. Next question, the member for London North Centre. Thank you, Speaker. Good morning. My question is to the Premier. Tenants in 1276 and 1280 Webster Street, many of whom who are elderly and on a fixed income need provincial intervention immediately. Members of the London City Council wrote a letter to urging Minister Clark to take immediate action to prevent the owners from renovicting vulnerable tenants and pushing them into precarious situations and homelessness. Talking points about ineffective, reactive, conservative legislation about fines won't keep these good people housed. It's simple. You have proactive legislation and rent control and tenant protection legislation on the table that we could pass today. Will this government stand up for seniors and others on Webster Street and pass NDP legislation to reinstate rent control immediately? The Associate Minister of Housing. Thank you, Speaker. I do want to thank the member for the questions. Mr Speaker, our government's top priority is supporting Ontario families. This includes not only helping first-time home buyers get into the market, but also protecting the rights of tenants. We have introduced the largest set of tenant protection reforms in Ontario's history as part of our helping home buyers protecting tenants plan. We doubled the maximum fines for breaking the law and strengthened protections against frivolous evictions like renovictions. When we're going to continue to work closely with municipalities to address their unique challenges, but we're going to maintain our laser focus on supporting families, job creators across this province, and I'll have more to say in the supplementary. Thank you. Thank you very much. Supplementary. Speaker, the Conservatives' answer to the housing affordability crisis is to get rid of rent control and sit back while tenants lose their homes. Waiting until they're evicted or living in their car is not a solution. Speaker, the landlord, Michael Klein, and family properties have a troubling history in their treatment of tenants. That's why Lennon City Council is asking you to act now. They're telling residents they can't have air conditioners, deliberately thumbing their nose at the Ontario Human Rights Tribunal and this government. If that weren't bad enough, they now want to charge tenants $200 per month for previously free parking. Elderly, vulnerable people on fixed income are being gouged. They need your action today. Will this government pass legislation to re-establish rent control and plug the hole of vacancy decontrol? Yes or no? The Associate Minister of Housing. Thank you, Speaker. Let me be clear. This government is standing with tenants and has taken the strongest action in Ontario's history to protect tenants from unfair rent increases. And that's why we kept the rent increase guideline at 2.5% this year, well below inflation. For tenants who do face improper increases above the guideline, they can recover those funds through the landlord tenant bottom. We just doubled the adjudicators on there. Our helping tenants package are going to double penalties for unlawfully hiking rents. We're strengthening those protections against rent evictions and we're giving tenants more rights, including the ability to have air conditioners in their units. But, however, if it was up to the NDP, we would have no housing supply, no rental property. It's this government that's getting housing built with the highest yet purpose rental build this year. And we're going to continue to do that for the people of Ontario so that we can all benefit. Thank you, Speaker. Next question, once again, the member for Brandt for Brandt. Thank you, Speaker. My question is for the Minister of Public and Business Service Delivery. Ontario is welcoming a record number of newcomers from around the world, including to my riding of Brandt for Brandt. It is important that these individuals and families have access to the services they need as they settle into communities across our province. I hear about concerns from individuals who are arriving, particularly those from Ukraine, as they have difficulty navigating the registration process for critical government programs. The challenges that they are experiencing are due to the limited services that certain local centres can provide. Everyone deserves to have convenient and seamless access to government services. Speaker, can the Minister please explain how our government is ensuring access to government services for all Ontarians? Mr. Public and Business Service Delivery. Thank you very much, Speaker. And I thank the member from Brandt for Brandt for his question. And I'm pleased to share with him that on June 14th, we are launching the new health car transaction harmonization pilot project to enhance the Ontario experience by better aligning public and private service centres. Speaker, Service Ontario is focusing on delivering essential government services for not only refugees and newcomers from Ukraine, but also residents returning to the province and the homeless population who currently cannot be registered at our local private service provider locations. Speaker, this Service Ontario pilot project launching in our great members' riding of Brandt for Brandt will provide through appointments, outreach services that meet the demand of new OHIP registrants and ensure that residents are able to access services they need conveniently and accessibly. Supplementary. Thank you, Speaker. And thank you to the minister and for his staff. I really appreciate his response, especially I've raised this issue with him just recently and we're finding a solution today. Across our province, the demand for different types of services varies according to each community's needs and population, whether it's long wait times or having the necessary requirements to obtain a service. We know that this can lead to frustration and delays. Ontarians should be able to resolve their issues and concerns at their first point of interaction with the government. The people of Ontario expect that our government will find solutions to fix the problems and challenges that they encounter. Speaker, can the minister please elaborate on the specific actions that our government is taking to improve the delivery of government services for the people of Ontario. Thank you. Mr. Public and Business Service Delivery. Thank you very much, Speaker. Under Premier's leadership, we made a promise to make life easier for Ontarians by improving access to our government services across the province. This new initiative is another new way we are delivering on that promise of better and more reliable services. Speaker, in addition to the harmonisation of services at existing service centres, my ministry is establishing Service Ontario Express locations to provide accessible core services and build a more sustainable in-person presence with streamlined process and minimise wait time. Speaker, the health car transaction harmonisation project is already supporting approximately 26,000 people through seven private service centres for health car services for international agri-food workers. Speaker, with the help of great members like the one from Brentford Brent that advocates for their communities, we are not stopping the work to make a trip to service Ontario easy, accessible, and of course, quick. Thank you. That concludes our question period for this morning.


Whenever any disaster happens, whether it happens through HIV or an accident or some other disease or a calamity, you know, whichever way it happens, how it happened is not the issue. Whenever a human being goes through a certain calamity in his life, which has brought about a certain level of suffering and a threat to life, the only thing that you can do is to strengthen yourself, to make yourself capable of dealing with situations. So when it comes, one thing is society is staying together and helping each other to come out of those situations. When the tsunami happened, everybody is reaching out. I don't understand why they are not reaching out to the HIV situation the same way with the same vigor. Why not? So in terms of prevention, whatever is being done is being done. But the true prevention only happens out of individual and social responsibility. It is not the medical infrastructure which can do this. The medical infrastructure can assist the society, but social and individual responsibility, more responsible ways of living is what can really change the situation. And above all, for those who have already been affected by the HIV infections, through whatever means it doesn't matter. First thing is to take away the social stigma attached to it so that the issue can be handled sensibly without wild emotional reactions to it. And one dimension of rehabilitation which I feel has not been taken care of is because if you want to rehabilitate a person from a debilitating situation like HIV infection, it's very important that it is handled on all levels physical, psychological, emotional and spiritual dimensions of the human being and of course considering the social aspect. Through yogic systems, we can put the life process to a new gear. We can put the life energies to a new level of vibrance through which the immune system will definitely respond better and whatever medication that one is taking will be much more effective if this technology could be made use of. This ancient science that has always been in this country has in many ways helped people to rejuvenate their systems from various kinds of diseases and life-defeating situations within themselves, both physiologically and psychologically. Though it is not a cure, definitely it could stabilize their system and give them a reasonable span of life.


Welcome back lecture 37. I think I think I looked at this yesterday. It was day 44 so today is day 45 of a 71 day semester. So we are certainly past the halfway point and headed toward the homestretch. So I gave the same message to my son. Now is not the time to coast or relax. Now is the time to start to put the foot on the accelerator because this is not the coasting or relaxing time of the semester. And that sound like something my dad should say. And he said oh, yeah dad. Okay. Yeah, that's really good. Where we eat? One thing I forgot to show you yesterday. I did mention it, but I forgot that I actually had this printed up. These models that we're working with whether it's a circuit with the L's and the R's and the 1 over C's or if it's a spring with the mass and the constant times the velocity which has to do with the viscosity of the fluid that the spring is in or the spring constant. These are kind of parallel equations. Second derivative term as a certain coefficient. First derivative term, certain coefficient. The original function, certain coefficient. And if there's a nice little chart in your supplement that talks about the parallel between these for the spring, the displacement or the amount of units it has traveled kind of its location. Q, the charge are really the same thing. So there's our original function in both x and q. Velocity, dx over dt, current derivative of the charge. So there's that term in the middle and then we've got the mass times acceleration and the L value times the derivative of the current which is second derivative of the charge. So you see a lot of parallels. It's the same mathematical model. So we've seen this before in mathematics whether it is y equals y0 e to the kt or a equals p times e to the rt. Different kind of visual appearances, but the same exact mathematical model. This is something growing or decaying exponentially. This is what is that? a equals p times e to the rt. Continuously compounded interest, right? But it is exactly the same mathematical model, just as these two are the same mathematical model. Alright, we're back to the book. Time permitting, we can go back and examine that, the end of that problem and see kind of where things went wrong on that number six problem from 7.9 web assign, but let's kind of do what we're supposed to do and see what time we have remaining to look at that problem. So in chapter 8, we're going to do sequences in series and we are about to experience one of the reasons why this particular course, Math 241, is perceived to be way more difficult than 141 or even 242 for that matter, is it is kind of choppy, is that we just finished doing a fairly significant introductory unit on second-order differential equations and now all of a sudden we switch horses completely, it seems like, and we go on to sequences in series. And that's not at all like, seemingly, what we did earlier in the semester, which is all the techniques of anti-differentiation, all that stuff that we did early. So it is kind of choppier in a sense, but they are loosely connected, not as strongly connected as the topics in Calc 1, and when you do Calc 3, you'll see that this course is not nearly as strongly connected as topics in Calc 3. So I think the choppiness factor enters into the perceived difficulty of this course. 8.1, which we'll look at today, and I think we can pretty much do justice to this today, is looking at sequences, and a sequence is just a list. So if it's got commas in there, we're talking about a sequence and not a series. If it's a series, we are talking about the indicated sum of these terms that are in the list. So it's just, first section is just a list. Now, why do we need to look at sequences if most of the rest, excuse me, rest of the chapter is talking about series, and when series converge and all kinds of convergence tests. In order for a series to converge, its sequence of partial sums has to converge. So if we don't first look at sequences, and what causes a sequence to converge, we're missing something basic in the background of what causes a series to converge. But when we look at the list, we're looking at what happens as we work our way out to the right. Those terms, way out there to the right, are they closing in on any one specific number? If they are, then it converges. If they are not, then it diverges. So we've already dealt with those things in terms of an integral, right? When an integral converges, we got a finite answer when it, we didn't get a finite answer, we said it diverged. So we will make some connections before we leave this chapter on convergent integrals and convergent series. In fact, one of the tests that we'll use is called an integral test. But that's later in chapter 8. So we have a list, a sub 1, or simply a, if you see a, that's the first term, a sub 2, you'll work your way up to a sub n, which would be the nth term of the sequence. The next term, just for notational purposes, would be a sub n plus 1. What would the preceding term be for a sub n? A sub n minus 1. So that's just a notational thing. So you can kind of pay attention to where the terms are in the series, in the sequence. If we have a sequence that is described, so the nth term of the sequence is described as n over 3n minus 1, we could generate that entire sequence and we could also decide if that sequence converges. So a sub 1 would be where n is 1, which is 1 half, a sub 2, where n is 2, and so on. So we've got this list going, what's the next term? We're not adding anything together yet. When n is 3, what do we get? 3 eighths. I don't know if it's obvious that as we progress from one term to the next, this particular sequence is convergent. So can you tell from the description the value to which we are converging? One third. One third, right? We've done limit problems like that. So we work our way out to the right as n approaches infinity. We examine kind of the shortcut. Normally we see x's here and x's here and x approaches infinity. It's the same limit problem, just n's in those positions. So the shortcut is, somebody tell me, what is the shortcut for this particular limit problem? Leading coefficients. We're going to use the leading coefficients when the degree is the same. So this is an n to the first. Down here we have an n to the first. So we've got 1n over 3n. Doesn't eventually the minus 1 become pretty insignificant as n approaches infinity. So as we look at these terms, as we work our way out to the right, they get closer and closer and closer to one third. Will we ever actually get to the value one third? No. I mean, you can put in n equals a thousand. And this would be 3 times a thousand minus 1, which is what? 2,000. 2,999. Is that pretty close to one third? Very close to one third. If you put in 100,000, you're going to get even closer. So it is a convergent sequence. Again, we're not addressing in this section. We're not adding any terms together. We're just looking at the value of that term as it progresses in this sequence way out to the right. Series, believe it or not, will also be able to converge. We'll be adding an infinite number of terms together.  But this is just what happens to this nth term way out to the right. I'm going to try to use some examples that show some things that we're going to encounter throughout this chapter. This has a couple different things that we're going to encounter. What do you think the negative one to the n does to this sequence as it progresses to the right? Part of this sequence. What does it do? It alternates the signs. And if you put in some different values, the first term would be negative one to the first. The second term, negative one squared. The third term, negative one cubed. So the alternating of signs could in fact become an issue. It kind of depends on what else is in that sequence. So negative one to the first, we get a negative, negative one squared. We get a positive, negative one cubed. We're back to negative. And they're going to alternate based on whether we have an even or an odd power of negative one. So let's look at the rest of this progression. So the numerator is increasing by one, one digit that we add to n. So it's getting larger. Isn't the denominator getting larger at a much larger rate? So we're going two over two, three over four. It may not be evident there, but now we've got four over eight. The next one would be what? Five over 16. So doesn't the denominator win in a sense? So when the denominator eventually wins, what happens to the part that I've circled here? It goes to zero. It goes to zero. So we've got stuff that may not be that evident when we start. So we've got, I'm going to go ahead and keep it two over two, three over four, four over eight. And I think we said it was going to be what? Five over 16. It may not be clear from the ones that we have thus far, but eventually the values of this particular sequence close in on zero. So the alternating signs don't become an issue that they might in another sequence because we're oscillating on either side of zero. So you can approach zero from either direction, positive and negative. And in a sense, if we're down here at one and up here, and then for the next one we're here and we're here, we are closing in on the value zero, but we're just doing so from positive values on the what? Even terms and negative values on the odd terms. It is possible to converge in that fashion. But if you just had an alternating sequence, let's say the sequence is just a to the n equals negative one to the n and that's it, that doesn't have any hope of convergence, right? Because you're going from negative one to one to negative one to one and so you're stuck in those two. Are we closing in on any one specific number? That would certainly by itself be divergent, even though this one is convergent. It converges to zero. It does so though. Some terms are positive, some terms are negative. You may encounter sequences or later descriptions of terms that we're going to add together, where it tells you that you can only use certain values. And this is all of these are functions of integers. The domain is the set of integers. So if we don't want to start with all integers, we better somehow put a little disclaimer here that says we don't want to start with all integers. We want n to be integers greater than or equal to two. So give me some terms of this particular sequence. When n is two, what do we get? Two. When n is three? Three and a half. When n is four? Four thirds. Four thirds, right? And we continue with that same process. I don't know if it's clear from these numbers, but we can always go back to the original description. Does this have a limit? As we pick integer values and keep working our way out to the right. One? Right? So it is a convergent sequence. One of the sequences mentioned, and this is hard to get an explicit formula. This would be an explicit formula that tells you if you want to find the 23rd term, you just put in 23 for n and if you want to find the 1,000th term, you put in 1,000 for n. Sometimes we don't have the luxury of an explicit description, and that would be the case with a Fibonacci sequence. So they actually do have a variety of ways that they model something, a Fibonacci sequence. So written out, it looks something like this. Has anybody dealt with a Fibonacci enough to tell how to arrive at 8th term, an individual term? What would the next term be? 21? Is that right? Where do you get 21? Add the two predecessors. So there's not a formula, so if we wanted to come out here and get the 39th term, there's not a formula we can put 39 in and generate the 39th term. So if we want the 39th term, we better have the 38th and the 37th. So we have to, in this setting, describe the first term, and it's not enough to just describe the first term. We also have to give a number to the second term. Now we can get the pattern to get the n plus 2 term. How do we get that? Don't we add the term before it, which would be n plus 1 to the term before that one, which would be n, right? So if we take the nth value of the nth term, add it to the n plus first term, we come up with that one. So if you don't like that notation, and you want to write it as a sub n, so it's described in terms of the nth term, we need the two predecessors, which are what? n minus 1 and n minus 2. So they both say the same thing. It just depends on how you prefer to write it. Most of the time, the preference is to write it in terms of the nth term, a sub n. All right, this is in the form of a definition. Let's see if I have those things ready. A sequence, a sub n, you can put the sequence in curly braces, since it's just a list anyway, it's a set. We separate the elements in the set with commas. So the sequence a sub n has the limit l, and we write, we've already done this a couple of times, the limit of a sub n is l, or a sub n approaches l as n approaches infinity. We know how to take limits, it talks about taking limits here, so that's not new. We say the sequence converges or is convergent. If it doesn't converge, then we call it divergent. That's terminology we've already used. Now, how can it converge? And by the way, these are dots, these are not connected curves because we're only using integer values for n, right? So we don't use n equals a third, or two thirds, or 17 20ths, or anything else. So that's why it's a collection of dots, as opposed to a curve. So it is possible for our points to kind of cross through the limiting value and approach it from the other side.  It is possible for it to oscillate on either side. This has a, what, a declining or decaying amplitude, so it could be a sine or cosine curve. This is possible as well, we kind of oscillate and approach zero from either side, or whatever the limiting value is. That's possible. Again, what we are concerned with is what happens way out here to the right, we don't really care how many times it crossed that limiting value, any of that stuff, we care what happens way out to the right. So that really technically is a definition, so we just kind of read it, accept it, and use it. Here's a theorem which requires some proof. It relates it to stuff that we've already done. So how our f of x and f of n, well if we say the description of the sequence is really some function of n, and we convert that to a function of x, that's really hard to do. Wherever there's an n, you put an x. And just like we used to take limits of functions, now how do functions differ? They connect the dots. So whether the dots are connected or not, we're still kind of rooting it or tying it to something we've already done. So if in fact the function has a limit as x approaches infinity, then the sequence, a sub n, has a limit as n approaches infinity. It's just that we are not connecting the dots. It's the integer values only on this diagram, not the connected curve. I don't know if I have a picture of that, yes I do. Occasionally we'll come up with a stubborn sequence that is difficult to analyze by itself, but we'll have some other ones, one that's bounded above by that one, another it's bounded below, and we'll be able to analyze those. Therefore, by the squeeze theorem, we'll be able to analyze what happens to the one in the middle. So again, these are dots. So here's the one kind of underneath the one in question. It seems to be convergent. The one that's bounding above is this one, which also appears to be convergent as we work our way out to the right. Here's the stubborn one, the b sub n, the one in the middle. We don't know what it's doing, but we know it's bounded by the other two. If the other two are convergent, and in fact convergent to the number L, then certainly the one in question in here that is doing some kind of unpredictable wavering, if it's bounded by those two, then it must also have the same limit as the other two. So that's the squeeze theorem for sequences. You don't need it very often, but occasionally you have a stubborn one in here that is bounded above and bounded below. If they have the same limit, we now know the limit to the one in the middle. So if the limit of a sub n and c sub n are both L, then the one in the middle must also be L. I guess this technically kind of results from the squeeze theorem. So if the limit of the absolute value of a function, not a function, a description of the nth term of the sequence is zero, then even without the absolute value, it should also be zero. So we're kind of closing in from either side, so certainly the one-sided version of that is also convergent. Let's say we have an nth term that is described as natural log of n over n, and we're trying to decide if it's convergent. Well, as n approaches infinity, doesn't the numerator get larger? Right? Infinitely large, so to speak. And as n approaches infinity, the denominator is just n, so certainly n approaches infinity. So if the numerator is getting infinitely large, I'm giving a big hint here, and the denominator gets infinitely large. Pardon? Because they increase at different rates. They increase at different rates. How do we handle infinity over infinity? Um... Lopitalz rule. Lopitalz rule. So anything that we've used to this point, we can also invoke with these as well. So this thing is headed toward infinity. This thing is headed toward infinity. So if we want the limit, as n approaches infinity, we can take the derivative of the top. What's the derivative of? And I know it may look awkward with the n's, if it bothers you just put an x there. The derivative of the natural log of n would be... What do you think is the case with this particular version of infinity over infinity? Which is faster? You think it's going to converge? Taking the natural log of a number, although it increases, it doesn't increase as fast as the number itself increases. Right? If you go from the natural log of 2 to the natural log of 3, yes, it increases, but not as much as you increase the denominator in going from 2 to 3. So the numerator is what? 1 over n. Denominator is 1. So we took the derivative of the top, derivative of the bottom. We reload. The limit of this is 0. Therefore, this sequence, the value of the terms as we work our way out to the right gets closer and closer to 0. Got to get a little factorial in there today. Factorial with sequences and series. In fact, we're going to deal with both of these later in chapter 8 on a pretty regular basis. What do you think? Which one? They both get fairly large fairly quickly. n factorial and n to the n. Which one gets larger faster? n to the n. n factorial. n to the n. Or n factorial. Well, let's write it out. The numerator is going to be something like 1 times 2 times 3 times 4. And it's going to go all the way up to n. Right? What's the denominator going to look like? So if it be 5 to the 5th, we'd have 5, 5 times. Right? So in terms of n, we'd have n used as a factor n times. Does that make sense? Because we're going to have a matching n underneath of it. So we're going to have factors of n, n times, and up here we have 1 times 2 times 3 all the way up to n. n to the n is bigger. Right? At a more rapid rate than n factorial. Now this follows in the textbook. It follows the squeeze theorem. Can you think of a series, not a series, a sequence that this is smaller than, isn't it smaller than 1 over n? This particular series is smaller than 1 over n. And even though we might have difficulty, I think we see this now when we have n's down here. Well, they only match up in the last place. Every other comparative value in the numerator is smaller than its matching value in the denominator. So clearly, the numerator is larger than this. But if you'll take kind of the rest of this other than 1 over n, I think it's pretty clear that the 1 in question, a sub n, is less than 1 over n. 1 over n already converges to 0. Therefore, this one must also converge to 0. Does that make sense? So this is one way that we could use the squeeze theorem. This one converges to 0. This one's even smaller. It must also converge to 0. So it's kind of being squeezed down by the one that is larger than it's bounded above by 1 over n. Therefore, this one must also converges to 0. Some of these things we really don't need right now. I'm trying to pick and choose as we go through this section. As it progressed out to the right, it was some number, R, and we do want to talk about what kind of R values are going to make sense in this problem. But the first term would be R to the 1, then R squared, R cubed, R to the fourth, and so on. It may not look like this ever has a chance to converge, but it does. What type of sequence is this where you multiply by R as you progress from one term to the next? We add anything like that? I'm trying to think if we've had something like that at this point in time. It's a geometric progression. So if you multiply by something as you go, so a geometric progression, and later in this chapter we're going to have geometric series. So we're going to want to add these things together. Right now we're just kind of analyzing what happens to the value of this term Well, let's take a real simple value. Let's say R is one. Well, if R is one, one, one squared, one cubed, one to the fourth, that's certainly convergent, right? I'm not talking about add them. I'm talking about the value of the term. Aren't we converging on the value one as we go? In fact, every one of them is one. So one ought to work if we ever expect this thing to converge. How about negative one? Negative one? This would be negative one. This would be positive one. This would be negative one. We're not converging to one specific number. They're alternating between one and negative one. So I don't think we want that one. So let's take the one category that the limit is one. If R itself is one, isn't it kind of absurd to examine values that cause this to get larger, like two or three or five, two squared, two cubed, two to the fourth? There's no way that's going to converge. So what types of numbers we looked at one? We looked at negative one. We think numbers like two, three, and four are a problem. In like fashion, negative two, negative three, and negative four are also problems. Don't they get larger in magnitude? Shouldn't we be examining values between negative one and one? So what do you think? Let's say our ratio is a half. So the first term is a half. Then we've got a half squared. Then we've got a half cubed. Think those would be converging on something? What? Zero. Let's take negative two-thirds. If R is negative two-thirds and you keep taking negative two-thirds to higher and higher powers, which one wins? Negative two to the 170th power or three to the 170th power? Three. Doesn't the denominator win? Numerators pretty large in magnitude but the denominator's much larger because it's a larger number that's raised to the 170th power. So even though these alternate in this area, aren't all of these values causing this particular geometric progression to converge? Is that right? And what would we say the limit would be? Zero? The value of the n-th term gets closer and closer and closer to zero as long as R is chosen anywhere in here and the other kind of strange value is when R is one, not a very interesting problem at all. It just stays at one, so the limit is one, but we also know that that is convergent. So if R is any other value, we would say this is a... this R to the n would be divergent. If R is any other value outside of here. So we could put them together and say that... but this will come in handy later in the chapter. Win is an infinite geometric series We're not there yet. Win is an infinite geometric series convergent. Right now it's just the sequence. If you set foot on our planet today for the very first day, you would probably know how to do these. So let's go through these real quickly. This is not anything of Earth-shattering magnitude. If you have a limit of a sum, it's the sum of the limits. The limit of a difference is the difference of the limits. We've already seen these, right? With functions, all these limit properties. If you have a constant times a function, you can farm the constant out in front. The limit of a product is the product of the limits. Ooh, there's one we almost forgot. It's a good thing we picked that one up. The limit of a constant is, in fact, that constant. Glad we got that one. The limit of a quotient is the quotient of the limits as long as the denominator doesn't do anything wacky. And the limit of something to a power is the limit of that function first, then raise that limit to a power. These are all things that we've done with functions. We now have the right to do all of those things with nth term descriptions of sequences. First part of this, we did the second part. Just as we describe functions that are increasing and decreasing, we can do the same thing with sequences. We did this already. This is where we decided when r to the n is convergent. So when is the sequence increasing? If the nth term is smaller than its successor, that's earth shattering for all n greater than or equal to 1. Just as a function is an increasing function, same thing with these terms in a sequence. When is it decreasing? If the nth term is larger than its predecessor for any term that you look at in this series. It is called, now that may be a new term, monotonic, is that a term that has come up before? Other than talking about your calculus professor that he talks in a monotone, I'm sorry about that. He's monotonic. If the whole function is either increasing or decreasing, it's called monotonic. It always is doing the same thing. So it doesn't increase for a while, then decrease for a while. That's not monotonic. If it's always increasing or always decreasing, this is a term that is used to describe it. So why is that word important? We'll put that monotonic together with this term bounded and we'll be able to come up with a conclusion. So what does bounded mean? A sequence is bounded above if there is a number m and there might be a lot of numbers m, but there just has to be one number m for this to be true, such that m is greater than or equal to any value of the sequence that you come up with at any point in time. It's bounded below, and again there might be a lot of different numbers, lower case m, but there's at least one number where m is less than or equal to every value of the sequence that we come up with. So for the entire sequence in both cases, if it's bounded above and bounded below, that actually happens some, then it is called a bounded sequence. Now let's put those two words together, bounded and monotonic. For the monotonic sequence theorem, every bounded monotonic sequence is convergent. So if you think about that, here's our capital M. We've got an increasing sequence. So it's monotonic because it's always increasing. This one is bounded above, doesn't it have to be convergent? Aren't we getting closer and closer and closer to this value capital M? Now aren't there other values that bound this sequence above?  There's another value that clearly is larger than every value that we come up with, but there only has to be one for it to be bounded above, and conveniently if it's bounded above by m, as in this picture, and its limit is also m, then it is a convergent sequence. All right, so that puts us to series, we should start tomorrow. Is there anything we can do in two or three minutes on that problem? I mean you have the c1 and c2 values, right? That worked and you tried them and they worked, and we can do that after class if necessary to see where that error is. All right, so that finishes 8-1. We will switch horses tomorrow and start with series, which now we're going to be adding terms up, which is a different kind of animal.


Four ways the narcissist keeps you locked in.  That's why they wanted to be around you They are drawn to powerful and attractive people It makes them feel powerful.  It's how they keep you locked in to Object of desire The narcissist keeps you locked in by breaking you down By making you think you're not as good as you think you are But they also don't want you to come to the conclusion That you may be better off elsewhere They want you to think that you're not good enough for anyone or anything They want you to think that your best hope is to stay with them And they will also present to you What they believe to be the object of your desire But they have to make it unattainable It has to be something that you cannot reach or achieve And they have to place it ten steps ahead of you at all times Because if you were ever to grasp it with your own hands You would realize that it doesn't even exist Or that it's not how they portrayed it to be But this is what they will use to keep you around And they will use it to motivate you to fulfill their desires and needs It makes you think that if you dedicate your life to the purpose that they have assigned to you One day you will achieve or obtain what you want But to make you think that way they have to trick you into thinking that they do have what you want When the reality is If they had what you wanted They would have given it to you a long time ago Because that would have locked you in more than anything else They can't give you what you want Because they don't even have it All they can do is present an illusion of something desirable to you Because that's enough to keep you locked in That's enough to keep you committed to them Free Isolation They have to isolate you They have to separate you from other people They have to make people think negatively of you And if that doesn't work They will try to make you think negatively of them It's divide and conquer They maintain control over you By encouraging dissent between you and other people Which then prevents you from uniting an opposition They cause you to remain alone or apart from other people Because then they can be your only source of influence It gives them the ability to brainwash you And keep you under their spell Because not only have they targeted yourself with self-esteem and made you doubt yourself But now they've also isolated you From anyone else who could tell you what's right So now your only source of information is the narcissist They can tell you whatever they want you to believe Whatever they think will further lock you under their control They have to try to make people think That you're dangerous or out of control Because that will further isolate you From people who could help you While giving the narcissist more influence and authority over you 4.


I am delighted to be part of the jury of exchange for media, the IDMA awards 2019. Digital media is emerging as one of the key platforms for delivering value to the customers. What's important is that the market year that the business leaders should ensure the strategic intent is well articulated with a high level of intrusive interest, involvement and persuasion to make the target audience respond in a competitively superior manner. As you all know digital marketing is just another tool for the execution of marketing strategy. I will be looking for digital marketing campaigns with creativity, sense of purpose that leverages and optimizes the unique capabilities of digital media in delivering and executing marketing strategy. I wish you all a good luck and pay the best campaign you will.


Hi everyone welcome back to my channel it's Eva from Bohemian Crafting and today I'm coming to share with you a channel which I just found and I got stuck on that channel for all afternoon. The name of the channel is Paper Paul and go to have a look. You know that I do love pop-up thingies. This guy is wow. He does the most amazing and surprising pop-ups I ever saw. Go to have a look. He does have few tutorials. I'm not through to all his videos yet I found first tutorial actually but I think he will have more I'm guessing hopefully. This is from one of his tutorials and I'm gonna follow his instructions. This is free download so I will put link down below for exact the video where I found this one but go to have a look to his videos. He does have mostly what I saw till now he does have showcase what he did. He makes like the professional pop-ups beautiful for books for collections. His work is amazing and this is from his tutorial how to make pop-up message and it's really beautiful. I did print it out. It's free template so I did print it out on a A4 size cardstock. This is 200 years some cardstock I'm gonna fast cut out and follow his instructions. They are very easy to follow. So first I supposed to score all lines which should be scored so I'm gonna take my scoring tool ruler and follow everything he says and I'm really looking forward to try this pop-up because I recently did kind of like pop-up hunt in my previous journal but it was made with totally different pop-up mechanisms so I'm gonna try this one you know to learn something new it's perfect all the time to learn something new so for those who would like to try it go to have a look link will be down below and definitely if you like if you like pop-up things go to check out this youtube channel he is amazing so subscribe to this wonderful crafter or artist because his mind wow like literally wow I'm impressed. So now next step is slide this into this so I'm gonna fold these little hinges down and go through to my card here this entry or opening come on good good good so here I supposed to unfold this like that ok and here we have that rest I do have here that shadow it's now less visible but I can still see that and on that shadow here on that spot I need to glue this one so I'm gonna put that glue and make exact position of that and I'm gonna let this dry I hope I'm on the right spot it did good stamping so I think it's glued and now I should fold it and here always when you work with pop-ups it's good if you will help to your pop-ups at the start to fold the right way so this should be folded down and slide under this kind of shape this one so I'm gonna fold it it's going there really nicely I have to say okay gonna take my home folder and press it a little bit that's amazing look at that okay help help help we help good yeah this I need help a little bit oh yeah it's going that it will be perfect and I forgot to stamp here so I'm gonna I'm gonna fold it this way and do some additional stamping and distressing I didn't realize this will be visible so I did my additional stamping and here I think this should be glued here to reinforce this flat so I'm gonna glue it there I'm gonna have a look on his tutorial if I'm doing everything right okay so first I'm gonna close the card and glue the back same as folded I'm gonna flip it this way and I'm gonna put the glue here on full top but I'm gonna leave this one open you know to give that space for that moving process so I think it's holding nicely this is so good okay it's really good I'm gonna help this and now I can glue this to reinforce that top flap so I'm gonna open it put the glue here and glue my reinforcement piece right here gonna let this dry and use my distress ink and distress all the edges all around and a little bit more stamping and I also added an eyelet so I can hung there some decoration look at that how beautiful is this one you are amazing yes Mr. Paul you are amazing this moving mechanism is pretty awesome it's simple yet very effective I like this mechanism very very much so now now you should place this in the card I'm not gonna place it in the card I just made from from fast food or not fast food from food packaging I made a little journal with my patreon so I'm gonna place it right here as decoration in my little pocket journal I'm gonna put the glue on that backside and glue it here on the pocket so then here will be a little pop-up message you are amazing and that's what we think about this one and it's all made by the way from that packaging so when you will have some takeaway do not throw it or bin it's very useful material now I'm gonna place it here let it dry and put there some decoration and before I go I'm gonna show you how my lovely opening envelope with that beautiful message you are amazing looks in my journal I added few grungy tags into those pockets around to make it even more interesting they are going really nicely together with this so I do have many other pockets here so I'm gonna create some other probably pop-up thingies in there so that's my sharing for today this was created by Paul his YouTube channel it's called paper Paul I will put link down below go to have a look and he does have also website so go to have a look on his informations very very talented artist I really love this idea and thank you so much for template and before I will say bye I would like to say huge thank you big big thank you to all of you who sent me wishes to my birthday I'm half century old right now I can't believe so thank you so much thank you so much guys for your amazing birthday wishes I really appreciate that very very much you made my day amazing thank you so much I wish you all wonderful days sending hooks to all of you and sending big thank you for thinking of me it's really amazing thank you have a wonderful day take care of yourself have a some nice amazing weekend and I will see you soon bye


Stanislaz to deliver, away to our right, raises left arm, delivers it now. Steve Cook goes to ground under challenge, but referee T&E not interested. Lewis Cook, lovely ball to Stanislaz, onside, square it goes, no! Just that little bit for United, Stanislaz the provider, Wilson scores for the seventh time this season, 1-0 Bournemouth. Here Sanchez for Jung on the right-hand side, Jung takes it to the corner of the penalty area. Sanchez now on the right, Sanchez across, chance for Martial!  Apologies for the technical gremlins on BBC Radio Solence, and John Murray in position from Five Live to call that Manchester United equaliser. What a disappointing moment as they all came down the right-hand side and Martial on the penalty spot there, with two men desperately throwing themselves in the way, but it came down the United right, and that is not what Bournemouth deserve, Willow, in his first 35 minutes. Pogba, left side of the penalty area here, faced by Steve Cook, Pogba getting to the byline, in comes across, Resford takes it down, Adam Smith's in there, and Marcus Resford has found a 90-second-minute winner, surely for Manchester United.