{"type":"video","version":"1.0","html":"<iframe src=\"https://www.loom.com/embed/c9858cda804541bd8b4a9757bd212a09\" frameborder=\"0\" width=\"1920\" height=\"1440\" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe>","height":1440,"width":1920,"provider_name":"Loom","provider_url":"https://www.loom.com","thumbnail_height":1440,"thumbnail_width":1920,"thumbnail_url":"https://cdn.loom.com/sessions/thumbnails/c9858cda804541bd8b4a9757bd212a09-f49726abf1fa1300.gif","duration":2046.04,"title":"Fundamentals of optimization (part not covered in class, ECON2125/6012, March 3)","description":"In this video, I explain the concepts of supremum and infimum, focusing on their definitions and importance in mathematical analysis. I discuss how these concepts apply to both closed and open sets, and I provide examples to illustrate their significance. I also touch on the relationship between these concepts and functions, emphasizing the conditions under which maxima and minima exist. Please take a moment to review the definitions and examples I provided, as they are crucial for our upcoming discussions."}