/*! * Dialogs Manager v4.9.3 * https://github.com/kobizz/dialogs-manager * * Copyright Kobi Zaltzberg * Released under the MIT license * https://github.com/kobizz/dialogs-manager/blob/master/LICENSE.txt */ (function($, global) { 'use strict'; /* * Dialog Manager */ var DialogsManager = { widgetsTypes: {}, createWidgetType: function(typeName, properties, Parent) { if (!Parent) { Parent = this.Widget; } var WidgetType = function() { Parent.apply(this, arguments); }; var prototype = WidgetType.prototype = new Parent(typeName); prototype.types = prototype.types.concat([typeName]); $.extend(prototype, properties); prototype.constructor = WidgetType; WidgetType.extend = function(typeName, properties) { return DialogsManager.createWidgetType(typeName, properties, WidgetType); }; return WidgetType; }, addWidgetType: function(typeName, properties, Parent) { if (properties && properties.prototype instanceof this.Widget) { return this.widgetsTypes[typeName] = properties; } return this.widgetsTypes[typeName] = this.createWidgetType(typeName, properties, Parent); }, getWidgetType: function(widgetType) { return this.widgetsTypes[widgetType]; } }; /* * Dialog Manager instances constructor */ DialogsManager.Instance = function() { var self = this, elements = {}, settings = {}; var initElements = function() { elements.body = $('body'); }; var initSettings = function(options) { var defaultSettings = { classPrefix: 'dialog', effects: { show: 'fadeIn', hide: 'fadeOut' } }; $.extend(settings, defaultSettings, options); }; this.createWidget = function(widgetType, properties) { var WidgetTypeConstructor = DialogsManager.getWidgetType(widgetType), widget = new WidgetTypeConstructor(widgetType); properties = properties || {}; widget.init(self, properties); return widget; }; this.getSettings = function(property) { if (property) { return settings[property]; } return Object.create(settings); }; this.init = function(settings) { initSettings(settings); initElements(); return self; }; self.init(); }; /* * Widget types constructor */ DialogsManager.Widget = function(widgetName) { var self = this, settings = {}, events = {}, elements = {}, hideTimeOut = 0, baseClosureMethods = ['refreshPosition']; var bindEvents = function() { var windows = [elements.window]; if (elements.iframe) { windows.push(jQuery(elements.iframe[0].contentWindow)); } windows.forEach(function(window) { if (settings.hide.onEscKeyPress) { window.on('keyup', onWindowKeyUp); } if (settings.hide.onOutsideClick) { window[0].addEventListener('click', hideOnOutsideClick, true); } if (settings.hide.onOutsideContextMenu) { window[0].addEventListener('contextmenu', hideOnOutsideClick, true); } if (settings.position.autoRefresh) { window.on('resize', self.refreshPosition); } }); if (settings.hide.onClick || settings.hide.onBackgroundClick) { elements.widget.on('click', hideOnClick); } }; var callEffect = function(intent, params) { var effect = settings.effects[intent], $widget = elements.widget; if ('function' === typeof effect) { effect.apply($widget, params); } else { if ($widget[effect]) { $widget[effect].apply($widget, params); } else { throw 'Reference Error: The effect ' + effect + ' not found'; } } }; var ensureClosureMethods = function() { var closureMethodsNames = baseClosureMethods.concat(self.getClosureMethods()); $.each(closureMethodsNames, function() { var methodName = this, oldMethod = self[methodName]; self[methodName] = function() { oldMethod.apply(self, arguments); }; }); }; var fixIframePosition = function(position) { if (! position.my) { return; } var horizontalOffsetRegex = /left|right/, extraOffsetRegex = /([+-]\d+)?$/, iframeOffset = elements.iframe.offset(), iframeWindow = elements.iframe[0].contentWindow, myParts = position.my.split(' '), fixedParts = []; if (myParts.length === 1) { if (horizontalOffsetRegex.test(myParts[0])) { myParts.push('center'); } else { myParts.unshift('center'); } } myParts.forEach(function(part, index) { var fixedPart = part.replace(extraOffsetRegex, function(partOffset) { partOffset = +partOffset || 0; if (! index) { partOffset += iframeOffset.left - iframeWindow.scrollX; } else { partOffset += iframeOffset.top - iframeWindow.scrollY; } if (partOffset >= 0) { partOffset = '+' + partOffset; } return partOffset; }); fixedParts.push(fixedPart); }); position.my = fixedParts.join(' '); }; var hideOnClick = function(event) { if (isContextMenuClickEvent(event)) { return; } if (settings.hide.onClick) { if ($(event.target).closest(settings.selectors.preventClose).length) { return; } } else if (event.target !== this) { return; } self.hide(); }; var isIgnoredTarget = function(event) { if (! settings.hide.ignore) { return false; } return !! $(event.target).closest(settings.hide.ignore).length; }; var hideOnOutsideClick = function(event) { if (isContextMenuClickEvent(event) || $(event.target).closest(elements.widget).length || isIgnoredTarget(event)) { return; } self.hide(); }; var initElements = function() { self.addElement('widget'); self.addElement('header'); self.addElement('message'); self.addElement('window', window); self.addElement('body', document.body); self.addElement('container', settings.container); if (settings.iframe) { self.addElement('iframe', settings.iframe); } if (settings.closeButton) { if ( settings.closeButtonClass ) { // Backwards compatibility settings.closeButtonOptions.iconClass = settings.closeButtonClass; } const $button = $('', settings.closeButtonOptions.attributes), $buttonIcon = $(settings.closeButtonOptions.iconElement).addClass(settings.closeButtonOptions.iconClass); $button.append($buttonIcon); self.addElement('closeButton', $button); } var id = self.getSettings('id'); if (id) { self.setID(id); } var classes = []; $.each(self.types, function() { classes.push(settings.classes.globalPrefix + '-type-' + this); }); classes.push(self.getSettings('className')); elements.widget .addClass(classes.join(' ')) .attr({ 'aria-modal': true, 'role': 'document', 'tabindex': 0, }); }; var initSettings = function(parent, userSettings) { var parentSettings = $.extend(true, {}, parent.getSettings()); settings = { headerMessage: '', message: '', effects: parentSettings.effects, classes: { globalPrefix: parentSettings.classPrefix, prefix: parentSettings.classPrefix + '-' + widgetName, preventScroll: parentSettings.classPrefix + '-prevent-scroll', }, selectors: { preventClose: '.' + parentSettings.classPrefix + '-prevent-close', }, container: 'body', preventScroll: false, iframe: null, closeButton: false, closeButtonOptions: { iconClass: parentSettings.classPrefix + '-close-button-icon', attributes: { role: 'button', 'tabindex': 0, 'aria-label': 'Close', href: '#', }, iconElement: '', }, position: { element: 'widget', my: 'center', at: 'center', enable: true, autoRefresh: false, }, hide: { auto: false, autoDelay: 5000, onClick: false, onOutsideClick: true, onOutsideContextMenu: false, onBackgroundClick: true, onEscKeyPress: true, ignore: '', }, }; $.extend(true, settings, self.getDefaultSettings(), userSettings); initSettingsEvents(); }; var initSettingsEvents = function() { $.each(settings, function(settingKey) { var eventName = settingKey.match(/^on([A-Z].*)/); if (!eventName) { return; } eventName = eventName[1].charAt(0).toLowerCase() + eventName[1].slice(1); self.on(eventName, this); }); }; var isContextMenuClickEvent = function(event) { // Firefox fires `click` event on every `contextmenu` event. return event.type === 'click' && event.button === 2; }; var normalizeClassName = function(name) { return name.replace(/([a-z])([A-Z])/g, function() { return arguments[1] + '-' + arguments[2].toLowerCase(); }); }; var onWindowKeyUp = function(event) { var ESC_KEY = 27, keyCode = event.which; if (ESC_KEY === keyCode) { self.hide(); } }; var unbindEvents = function() { var windows = [elements.window]; if (elements.iframe) { windows.push(jQuery(elements.iframe[0].contentWindow)); } windows.forEach(function(window) { if (settings.hide.onEscKeyPress) { window.off('keyup', onWindowKeyUp); } if (settings.hide.onOutsideClick) { window[0].removeEventListener('click', hideOnOutsideClick, true); } if (settings.hide.onOutsideContextMenu) { window[0].removeEventListener('contextmenu', hideOnOutsideClick, true); } if (settings.position.autoRefresh) { window.off('resize', self.refreshPosition); } }); if (settings.hide.onClick || settings.hide.onBackgroundClick) { elements.widget.off('click', hideOnClick); } }; this.addElement = function(name, element, classes) { var $newElement = elements[name] = $(element || '
'), normalizedName = normalizeClassName(name); classes = classes ? classes + ' ' : ''; classes += settings.classes.globalPrefix + '-' + normalizedName; classes += ' ' + settings.classes.prefix + '-' + normalizedName; $newElement.addClass(classes); return $newElement; }; this.destroy = function() { unbindEvents(); elements.widget.remove(); self.trigger('destroy'); return self; }; this.getElements = function(item) { return item ? elements[item] : elements; }; this.getSettings = function(setting) { var copy = Object.create(settings); if (setting) { return copy[setting]; } return copy; }; this.hide = function() { if (! self.isVisible()) { return; } clearTimeout(hideTimeOut); callEffect('hide', arguments); unbindEvents(); if (settings.preventScroll) { self.getElements('body').removeClass(settings.classes.preventScroll); } self.trigger('hide'); return self; }; this.init = function(parent, properties) { if (!(parent instanceof DialogsManager.Instance)) { throw 'The ' + self.widgetName + ' must to be initialized from an instance of DialogsManager.Instance'; } ensureClosureMethods(); self.trigger('init', properties); initSettings(parent, properties); initElements(); self.buildWidget(); self.attachEvents(); self.trigger('ready'); return self; }; this.isVisible = function() { return elements.widget.is(':visible'); }; this.on = function(eventName, callback) { if ('object' === typeof eventName) { $.each(eventName, function(singleEventName) { self.on(singleEventName, this); }); return self; } var eventNames = eventName.split(' '); eventNames.forEach(function(singleEventName) { if (!events[singleEventName]) { events[singleEventName] = []; } events[singleEventName].push(callback); }); return self; }; this.off = function(eventName, callback) { if (! events[ eventName ]) { return self; } if (! callback) { delete events[eventName]; return self; } var callbackIndex = events[eventName].indexOf(callback); if (-1 !== callbackIndex) { events[eventName].splice(callbackIndex, 1); } return self; }; this.refreshPosition = function() { if (! settings.position.enable) { return; } var position = $.extend({}, settings.position); if (elements[position.of]) { position.of = elements[position.of]; } if (! position.of) { position.of = window; } if (settings.iframe) { fixIframePosition(position); } elements[position.element].position(position); }; this.setID = function(id) { elements.widget.attr('id', id); return self; }; this.setHeaderMessage = function(message) { self.getElements('header').html(message); return self; }; this.setMessage = function(message) { elements.message.html(message); return self; }; this.setSettings = function(key, value) { if (jQuery.isPlainObject(value)) { $.extend(true, settings[key], value); } else { settings[key] = value; } return self; }; this.show = function() { clearTimeout(hideTimeOut); elements.widget.appendTo(elements.container).hide(); callEffect('show', arguments); self.refreshPosition(); if (settings.hide.auto) { hideTimeOut = setTimeout(self.hide, settings.hide.autoDelay); } bindEvents(); if (settings.preventScroll) { self.getElements('body').addClass(settings.classes.preventScroll); } self.trigger('show'); return self; }; this.trigger = function(eventName, params) { var methodName = 'on' + eventName[0].toUpperCase() + eventName.slice(1); if (self[methodName]) { self[methodName](params); } var callbacks = events[eventName]; if (!callbacks) { return; } $.each(callbacks, function(index, callback) { callback.call(self, params); }); return self; }; }; DialogsManager.Widget.prototype.types = []; // Inheritable widget methods DialogsManager.Widget.prototype.buildWidget = function() { var elements = this.getElements(), settings = this.getSettings(); elements.widget.append(elements.header, elements.message); this.setHeaderMessage(settings.headerMessage); this.setMessage(settings.message); if (this.getSettings('closeButton')) { elements.widget.prepend(elements.closeButton); } }; DialogsManager.Widget.prototype.attachEvents = function() { var self = this; if (self.getSettings('closeButton')) { self.getElements('closeButton').on('click', function(event) { event.preventDefault(); self.hide(); }); } }; DialogsManager.Widget.prototype.getDefaultSettings = function() { return {}; }; DialogsManager.Widget.prototype.getClosureMethods = function() { return []; }; DialogsManager.Widget.prototype.onHide = function() { }; DialogsManager.Widget.prototype.onShow = function() { }; DialogsManager.Widget.prototype.onInit = function() { }; DialogsManager.Widget.prototype.onReady = function() { }; DialogsManager.widgetsTypes.simple = DialogsManager.Widget; DialogsManager.addWidgetType('buttons', { activeKeyUp: function(event) { var TAB_KEY = 9; if (event.which === TAB_KEY) { event.preventDefault(); } if (this.hotKeys[event.which]) { this.hotKeys[event.which](this); } }, activeKeyDown: function(event) { if (!this.focusedButton) { return; } var TAB_KEY = 9; if (event.which === TAB_KEY) { event.preventDefault(); var currentButtonIndex = this.focusedButton.index(), nextButtonIndex; if (event.shiftKey) { nextButtonIndex = currentButtonIndex - 1; if (nextButtonIndex < 0) { nextButtonIndex = this.buttons.length - 1; } } else { nextButtonIndex = currentButtonIndex + 1; if (nextButtonIndex >= this.buttons.length) { nextButtonIndex = 0; } } this.focusedButton = this.buttons[nextButtonIndex].trigger('focus'); } }, addButton: function(options) { var self = this, settings = self.getSettings(), buttonSettings = jQuery.extend(settings.button, options); var classes = options.classes ? options.classes + ' ' : ''; classes += settings.classes.globalPrefix + '-button'; var $button = self.addElement(options.name, $('<' + buttonSettings.tag + '>').html(options.text), classes); self.buttons.push($button); var buttonFn = function() { if (settings.hide.onButtonClick) { self.hide(); } if ('function' === typeof options.callback) { options.callback.call(this, self); } }; $button.on('click', buttonFn); if (options.hotKey) { this.hotKeys[options.hotKey] = buttonFn; } this.getElements('buttonsWrapper').append($button); if (options.focus) { this.focusedButton = $button; } return self; }, bindHotKeys: function() { this.getElements('window').on({ keyup: this.activeKeyUp, keydown: this.activeKeyDown }); }, buildWidget: function() { DialogsManager.Widget.prototype.buildWidget.apply(this, arguments); var $buttonsWrapper = this.addElement('buttonsWrapper'); this.getElements('widget').append($buttonsWrapper); }, getClosureMethods: function() { return [ 'activeKeyUp', 'activeKeyDown' ]; }, getDefaultSettings: function() { return { hide: { onButtonClick: true }, button: { tag: 'button' } }; }, onHide: function() { this.unbindHotKeys(); }, onInit: function() { this.buttons = []; this.hotKeys = {}; this.focusedButton = null; }, onShow: function() { this.bindHotKeys(); if (!this.focusedButton) { this.focusedButton = this.buttons[0]; } if (this.focusedButton) { this.focusedButton.trigger('focus'); } }, unbindHotKeys: function() { this.getElements('window').off({ keyup: this.activeKeyUp, keydown: this.activeKeyDown }); } }); DialogsManager.addWidgetType('lightbox', DialogsManager.getWidgetType('buttons').extend('lightbox', { getDefaultSettings: function() { var settings = DialogsManager.getWidgetType('buttons').prototype.getDefaultSettings.apply(this, arguments); return $.extend(true, settings, { contentWidth: 'auto', contentHeight: 'auto', position: { element: 'widgetContent', of: 'widget', autoRefresh: true } }); }, buildWidget: function() { DialogsManager.getWidgetType('buttons').prototype.buildWidget.apply(this, arguments); var $widgetContent = this.addElement('widgetContent'), elements = this.getElements(); $widgetContent.append(elements.header, elements.message, elements.buttonsWrapper); elements.widget.html($widgetContent); if (elements.closeButton) { $widgetContent.prepend(elements.closeButton); } }, onReady: function() { var elements = this.getElements(), settings = this.getSettings(); if ('auto' !== settings.contentWidth) { elements.message.width(settings.contentWidth); } if ('auto' !== settings.contentHeight) { elements.message.height(settings.contentHeight); } } })); DialogsManager.addWidgetType('confirm', DialogsManager.getWidgetType('lightbox').extend('confirm', { onReady: function() { DialogsManager.getWidgetType('lightbox').prototype.onReady.apply(this, arguments); var strings = this.getSettings('strings'), isDefaultCancel = this.getSettings('defaultOption') === 'cancel'; this.addButton({ name: 'cancel', text: strings.cancel, callback: function(widget) { widget.trigger('cancel'); }, focus: isDefaultCancel }); this.addButton({ name: 'ok', text: strings.confirm, callback: function(widget) { widget.trigger('confirm'); }, focus: !isDefaultCancel }); }, getDefaultSettings: function() { var settings = DialogsManager.getWidgetType('lightbox').prototype.getDefaultSettings.apply(this, arguments); settings.strings = { confirm: 'OK', cancel: 'Cancel' }; settings.defaultOption = 'cancel'; return settings; } })); DialogsManager.addWidgetType('alert', DialogsManager.getWidgetType('lightbox').extend('alert', { onReady: function() { DialogsManager.getWidgetType('lightbox').prototype.onReady.apply(this, arguments); var strings = this.getSettings('strings'); this.addButton({ name: 'ok', text: strings.confirm, callback: function(widget) { widget.trigger('confirm'); } }); }, getDefaultSettings: function() { var settings = DialogsManager.getWidgetType('lightbox').prototype.getDefaultSettings.apply(this, arguments); settings.strings = { confirm: 'OK' }; return settings; } })); // Exporting the DialogsManager variable to global global.DialogsManager = DialogsManager; })( typeof jQuery !== 'undefined' ? jQuery : typeof require === 'function' && require('jquery'), (typeof module !== 'undefined' && typeof module.exports !== 'undefined') ? module.exports : window ); {"id":11932,"date":"2023-06-24T11:39:50","date_gmt":"2023-06-24T11:39:50","guid":{"rendered":"https:\/\/weeklypostgazette.com\/?p=11932"},"modified":"2023-06-24T11:39:50","modified_gmt":"2023-06-24T11:39:50","slug":"understanding-interval-notation-a-comprehensive-guide","status":"publish","type":"post","link":"https:\/\/weeklypostgazette.com\/understanding-interval-notation-a-comprehensive-guide\/","title":{"rendered":"Understanding Interval Notation A Comprehensive Guide"},"content":{"rendered":"

Interval notation is a powerful mathematical tool used to represent intervals on the number line. It provides a concise and precise way to express sets of numbers and is commonly used in various branches of mathematics, including calculus, algebra, and statistics. In this article, we will delve into the intricacies of interval notation<\/a>, exploring its different components and the various types of intervals it can represent. By the end, you will have a solid understanding of interval notation and its significance in mathematics.<\/p>\n

What is Interval Notation?<\/h2>\n

Interval notation is a shorthand method for expressing intervals as sets of numbers. It involves using parentheses, brackets, and symbols to denote the boundaries of an interval. The basic form of interval notation is [a, b], where a and b are real numbers representing the lower and upper bounds, respectively.<\/p>\n

Open Intervals:<\/h3>\n

An open interval is represented by (a, b). Where a and b are real numbers. This notation indicates that the interval includes all numbers between a and b, excluding both endpoints. For example, the interval (0, 1) represents all real numbers greater than 0 and less than 1.<\/p>\n

Closed Intervals:<\/h3>\n

A closed interval is represented by [a, b], where a and b are real numbers. This notation indicates that the interval includes all numbers between a and b, including both endpoints. For example, the interval [0, 1] represents all real numbers greater than or equal to 0 and less than or equal to 1.<\/p>\n

Half-Open or Half-Closed Intervals:<\/h2>\n

A half-open or half-closed interval is represented by various combinations of parentheses and brackets. For example, [a, b) represents an interval that includes a but excludes b, while (a, b] represents an interval that includes b but excludes a. These notations are useful in specific mathematical contexts and allow for more precise descriptions of intervals.<\/p>\n

Infinite Intervals:<\/h2>\n

Interval notation can also be used to represent infinite intervals. For example, (-\u221e, a) represents all real numbers less than a, and (b, \u221e) represents all real numbers greater than b. These notations are particularly valuable in calculus and analysis.<\/p>\n

Union and Intersection of Intervals:<\/h2>\n

Interval notation allows for the representation of unions and intersections of intervals. The union of two intervals, [a, b] \u222a [c, d], represents the set of numbers that belong to either interval. The intersection of two intervals, [a, b] \u2229 [c, d], represents the set of numbers that belong to both intervals. These operations play a fundamental role in solving mathematical problems involving intervals.<\/p>\n

Conclusion:<\/h3>\n

Interval notation is an essential tool for mathematicians, providing a concise and standardized way to represent intervals. Whether working with open intervals, closed intervals, half-open intervals, or infinite intervals, understanding interval notation allows for clear and precise communication in mathematical discourse. By mastering interval notation, you gain the ability to express intervals accurately, enabling you to solve a wide range of mathematical problems with ease.<\/p>\n","protected":false},"excerpt":{"rendered":"

Interval notation is a powerful mathematical tool used to represent intervals on the number line. It provides a concise and precise way to express sets of numbers and is commonly used in various branches of mathematics, including calculus, algebra, and statistics. In this article, we will delve into the intricacies of interval notation, exploring its […]<\/p>\n","protected":false},"author":2,"featured_media":11933,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[22],"tags":[9864,9859,9862,9860,9855,9856,9861,9863,9858,9857],"class_list":["post-11932","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-news","tag-domain-and-range-interval-notation","tag-domain-in-interval-notation","tag-domain-interval-notation","tag-how-to-write-interval-notation","tag-interval-notation","tag-interval-notation-calculator","tag-interval-notation-domain","tag-interval-notation-domain-and-range","tag-interval-notation-example","tag-what-is-interval-notation"],"yoast_head":"\nUnderstanding Interval Notation A Comprehensive Guide<\/title>\n<meta name=\"description\" content=\"Interval notation is an essential tool for mathematicians, providing a concise and standardized way to represent intervals.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/weeklypostgazette.com\/understanding-interval-notation-a-comprehensive-guide\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Understanding Interval Notation A Comprehensive Guide\" \/>\n<meta property=\"og:description\" content=\"Interval notation is an essential tool for mathematicians, providing a concise and standardized way to represent intervals.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/weeklypostgazette.com\/understanding-interval-notation-a-comprehensive-guide\/\" \/>\n<meta property=\"og:site_name\" content=\"Weekly Post Gazette\" \/>\n<meta property=\"article:published_time\" content=\"2023-06-24T11:39:50+00:00\" \/>\n<meta property=\"og:image\" 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