{"id":246586,"date":"2025-07-07T09:12:42","date_gmt":"2025-07-07T09:12:42","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=246586"},"modified":"2025-07-07T09:12:43","modified_gmt":"2025-07-07T09:12:43","slug":"what-are-integers-closed-under-the-operation-of-subtraction-while-the-whole-numbers-are-no","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/07\/what-are-integers-closed-under-the-operation-of-subtraction-while-the-whole-numbers-are-no\/","title":{"rendered":"what are integers closed under the operation of subtraction while the whole numbers are no"},"content":{"rendered":"\n<p>what are integers closed under the operation of subtraction while the whole numbers are no<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The concept of closure under an operation refers to whether performing that operation on elements within a set always results in an element that is also within the same set.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Integers and Subtraction<\/h3>\n\n\n\n<p>Integers are the set of whole numbers and their negatives, which include {&#8230;, -3, -2, -1, 0, 1, 2, 3, &#8230;}. Integers are closed under subtraction, meaning that when you subtract any two integers, the result will always be another integer. For example:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>5\u22123=25 &#8211; 3 = 25\u22123=2, and both 5 and 3 are integers, as well as the result, 2.<\/li>\n\n\n\n<li>\u22122\u22124=\u22126-2 &#8211; 4 = -6\u22122\u22124=\u22126, and both -2 and 4 are integers, as well as the result, -6.<\/li>\n<\/ul>\n\n\n\n<p>In these examples, performing subtraction on integers results in another integer, which shows that integers are closed under subtraction.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Whole Numbers and Subtraction<\/h3>\n\n\n\n<p>Whole numbers, on the other hand, are the set of non-negative integers: {0, 1, 2, 3, 4, &#8230;}. Whole numbers are <em>not<\/em> closed under subtraction. This is because subtracting one whole number from another can result in a negative number, which is not a whole number. For example:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>3\u22125=\u221223 &#8211; 5 = -23\u22125=\u22122, which is not a whole number since it is negative.<\/li>\n\n\n\n<li>0\u22121=\u221210 &#8211; 1 = -10\u22121=\u22121, which is also not a whole number.<\/li>\n<\/ul>\n\n\n\n<p>Therefore, subtracting whole numbers does not always yield a whole number, making the set of whole numbers <em>not<\/em> closed under subtraction.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Key Differences in Closure<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Integers<\/strong>: When subtracting any two integers, the result is always an integer, so integers are closed under subtraction.<\/li>\n\n\n\n<li><strong>Whole numbers<\/strong>: When subtracting larger numbers from smaller ones, the result can be negative, which is not a whole number. Hence, whole numbers are not closed under subtraction.<\/li>\n<\/ul>\n\n\n\n<p>This difference illustrates why the set of integers is closed under subtraction, while the set of whole numbers is not.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-893.jpeg\" alt=\"\" class=\"wp-image-246587\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>what are integers closed under the operation of subtraction while the whole numbers are no The Correct Answer and Explanation is: The concept of closure under an operation refers to whether performing that operation on elements within a set always results in an element that is also within the same set. Integers and Subtraction Integers [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","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":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-246586","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/246586","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=246586"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/246586\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=246586"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=246586"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=246586"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}