{"id":9508,"date":"2022-01-15T21:25:50","date_gmt":"2022-01-15T15:55:50","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9508"},"modified":"2022-01-16T17:15:42","modified_gmt":"2022-01-16T11:45:42","slug":"finite-sets-and-infinite-sets-definition-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/finite-sets-and-infinite-sets-definition-examples\/","title":{"rendered":"Finite Sets and Infinite Sets – Definition and Examples"},"content":{"rendered":"

Here you will learn what are finite and infinite sets, cardinality of a finite set and examples based on it.<\/p>\n

Let’s begin –<\/p>\n

Finite and Infinite Sets<\/h2>\n

(i) Finite Sets<\/strong><\/h4>\n

A set is called a finite set if it is either void set or its element can be listed (counted, labelled) by natural numbers 1, 2, 3, ….. and the process of listing terminates at a certain natural number n (say).<\/p>\n

Cardinal Number of a Finite Set<\/strong><\/h4>\n

The number n in the above definition is called the cardinal number or order of a finite set A and is denoted by n(A).<\/p>\n

Example<\/strong><\/span> : Each one of the following sets is a finite set :<\/p>\n

(i)  Set of even natural numbers less than 100.<\/p>\n

(ii)  Set of soldiers in Indian army<\/p>\n

(iii) Set of even prime natural numbers<\/p>\n

(iii) Set of all persons on the earth<\/p>\n

(ii) Infinite Set<\/strong><\/h4>\n

A set whose elements cannot be listed by the natural numbers 1, 2, 3, …. n for any natural number n is called an infinite set.<\/p>\n

Example<\/strong><\/span> : Each one of the following sets is an infinite set :<\/p>\n

(i)  Set of all points in a plane.<\/p>\n

(ii)  Set of lines in a plane<\/p>\n

(iii) {x \\(\\in\\) R : 0 < x < 1}<\/p>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what are finite and infinite sets, cardinality of a finite set and examples based on it. Let’s begin – Finite and Infinite Sets (i) Finite Sets A set is called a finite set if it is either void set or its element can be listed (counted, labelled) by natural numbers 1, …<\/p>\n

Finite Sets and Infinite Sets – Definition and Examples<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[16],"tags":[743,745,744],"yoast_head":"\nFinite Sets and Infinite Sets - Definition and Examples<\/title>\n<meta name=\"description\" content=\"In this post you will learn what are finite and infinite sets, cardinality of a finite set and examples based on it.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/finite-sets-and-infinite-sets-definition-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Finite Sets and Infinite Sets - 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