{"id":1086,"date":"2017-10-11T19:32:29","date_gmt":"2017-10-11T23:32:29","guid":{"rendered":"http:\/\/blog.richmond.edu\/math320\/?p=1086"},"modified":"2017-10-15T01:12:23","modified_gmt":"2017-10-15T05:12:23","slug":"what-happened-10102017","status":"publish","type":"post","link":"https:\/\/blog.richmond.edu\/math320\/2017\/10\/11\/what-happened-10102017\/","title":{"rendered":"What happened 10\/10\/2017"},"content":{"rendered":"

We began today’s class by going through the challenge problems. While we were talking about problem number 3, an interesting issue came up, which is how do we define the domain of a function. After our discussion, we found out that the domain of a function is not determined by the formula. Instead, the domain is just defined by us. If we say a function f maps from R to R, then the domain of f is R despite the fact that there is certain element in R that f is not defined with.<\/p>\n

After we finished talking about the challenge problems, we moved on to our lecture and learned the way of proving functional limit using precise definition. The example we have is to prove \"\lim_{x\rightarrow\frac{1}{3}}. One thing that needs to be paid attention to in this example is that, even though we have \"x-\frac{1}{3}<\frac{\epsilon}{18}\", we should still choose \"\delta.<\/p>\n

Finally, we talked about theorem 4.2.3, which states that Given \"f:A\rightarrow\mathbb{R}\" and $c\\in L(A)$. \"\lim_{x\rightarrow if and only if \"\forall such that \"x_n\neq and \"(x_n)\rightarrow.<\/p>\n","protected":false},"excerpt":{"rendered":"

We began today’s class by going through the challenge problems. While we were talking about problem number 3, an interesting issue came up, which is how do we define the domain of a function. After our discussion, we found out that the domain of a function is not determined by the formula. Instead, the domain […]<\/p>\n","protected":false},"author":3537,"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-1086","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-hw","jetpack-related-posts":[],"_links":{"self":[{"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/posts\/1086","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\/3537"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/comments?post=1086"}],"version-history":[{"count":0,"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/posts\/1086\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/media?parent=1086"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/categories?post=1086"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/tags?post=1086"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}