We began class today with a Weekly Situation. This situation was about what we can say about the set (a,b) from definitions versus what we can say using known theorems, lemmas, and homework results. We finished our discussion of Chapter 3 by proving part of the Heine-Borel Theorem. There are three statements in the Heine-Borel Theorem that are equivalent. We proved that K is compact if and only if K is closed and bounded. We also stated the Nested Compact Set Property. We also began Chapter 4 today. We defined functional limit and learned how to prove what the limit of a function is. Then, we talked about a few examples of limits that do not exist. Finally, we discussed the “largest possible delta” method, which we will continue on Thursday.<\/p>\n","protected":false},"excerpt":{"rendered":"
We began class today with a Weekly Situation. This situation was about what we can say about the set (a,b) from definitions versus what we can say using known theorems, lemmas, and homework results. We finished our discussion of Chapter 3 by proving part of the Heine-Borel Theorem. There are three statements in the Heine-Borel […]<\/p>\n","protected":false},"author":3530,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[58821],"tags":[],"class_list":["post-972","post","type-post","status-publish","format-standard","hentry","category-what-happened-today"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p7L4E1-fG","jetpack-related-posts":[],"_links":{"self":[{"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/posts\/972","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/users\/3530"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/comments?post=972"}],"version-history":[{"count":0,"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/posts\/972\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/media?parent=972"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/categories?post=972"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/tags?post=972"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}