{"id":5041,"date":"2012-11-30T03:01:58","date_gmt":"2012-11-30T03:01:58","guid":{"rendered":"http:\/\/SchoolTutoring.com\/help\/?p=5041"},"modified":"2014-12-02T08:31:55","modified_gmt":"2014-12-02T08:31:55","slug":"intervals-and-neighbourhoods","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/intervals-and-neighbourhoods\/","title":{"rendered":"Intervals and Neighbourhoods"},"content":{"rendered":"

If a<\/em><\/strong> and b<\/em><\/strong> are any two real numbers such that a<\/em><\/strong> is less than b<\/em><\/strong> (a<b<\/em><\/strong>). Then the set {x\u20ac R\/ a\u2264 x \u2264 b} is called a closed<\/em><\/strong> interval with end points a<\/em><\/strong> and b<\/em><\/strong> and is denoted by [a,b]. The set {x \u20ac R\/a<x<b} is called an open<\/em><\/strong> interval with end points a<\/em><\/strong> and b <\/em><\/strong>and is denoted by (a,b).<\/p>\n

Thus,<\/p>\n[a,b] = {x\u20ac R\/ a\u2264 x \u2264 b} and<\/p>\n

(a,b) = {x \u20ac R\/a<x<b}<\/p>\n

Similarly we can define some other intervals as follows.<\/p>\n

(a,b] = {x\u20ac R\/ a< x \u2264 b}<\/p>\n[a,b) \u00a0= {x\u20ac R\/ a\u2264 x < b}<\/p>\n

In these 4 intervals, the length of the interval is finite which is defined by b-a<\/em><\/strong>.<\/p>\n[a, \u221e) = {x\u20ac R\/ x\u2265a}<\/p>\n

(a, \u221e) = {x\u20ac R\/ x>a}<\/p>\n

(-\u221e,a] = {x\u20ac R\/ x\u2264a}<\/p>\n

(-\u221e,a) = {x\u20ac R\/ x<a}<\/p>\n

In these 4 intervals, we cannot define the length and hence these 4 intervals are of infinite length.<\/p>\n

Neighbourhoods:<\/strong><\/p>\n

Let a be any real number. If p>0 then the open interval (a-p, a+p) is called the p-neighbourhood of a. The following figure shows the location of (a-p, a+p) on the number line.<\/p>\n

\"\"<\/a><\/p>\n

The set obtained by deleting a from this neighbourhood is called the deleted p-neighbourhood of a.i.e. the deleted p-neighbourhood of a is<\/p>\n

(a,p, a) U (a,a+p) or (a-p, a+p) \u2013{a}.<\/p>\n

Tutors for Spanish<\/a> are also available if you need more help.<\/p>\n

SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Florida visit: Tutoring in Florida. <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

If a and b are any two real numbers such that a is less than b (a<b). Then the set {x\u20ac R\/ a\u2264 x \u2264 b} is called a closed interval with end points a and b and is denoted by [a,b]. The set {x \u20ac R\/a<x<b} is called an open interval with end points […]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[297,663,937,961,1025,1188,1245],"class_list":["post-5041","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-closed","tag-finite","tag-infinite","tag-interval","tag-length","tag-neigbourhood","tag-open"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/5041","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=5041"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/5041\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=5041"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=5041"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=5041"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}