Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; plgContentJComments has a deprecated constructor in /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php on line 25 Call Stack: 0.0001 360976 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.0745 1211272 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.0745 1211272 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.1485 4197424 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.1499 4225232 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.1506 4242944 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.1508 4273464 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.1518 4296184 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.1518 4296184 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.1995 4968376 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.2030 5160528 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.2035 5181456 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.2156 5392624 13. Joomla\CMS\Plugin\PluginHelper::importPlugin() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:189 0.2156 5392880 14. Joomla\CMS\Plugin\PluginHelper::import() /var/www/astarmathsandphysics/libraries/src/Plugin/PluginHelper.php:182 Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; JCommentsACL has a deprecated constructor in /var/www/astarmathsandphysics/components/com_jcomments/classes/acl.php on line 17 Call Stack: 0.0001 360976 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.0745 1211272 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.0745 1211272 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.1485 4197424 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.1499 4225232 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.1506 4242944 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.1508 4273464 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.1518 4296184 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.1518 4296184 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.1995 4968376 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.2030 5160528 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.2035 5181456 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.3525 13814632 13. JEventDispatcher->trigger() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:199 0.3528 13815032 14. plgContentJComments->update() /var/www/astarmathsandphysics/libraries/joomla/event/dispatcher.php:160 0.3528 13815032 15. plgContentJComments->onContentAfterDisplay() /var/www/astarmathsandphysics/libraries/joomla/event/event.php:70 0.3530 13823280 16. plgContentJComments->onAfterDisplayContent() /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php:339 0.3532 13825016 17. JComments::show() /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php:282 0.3538 13858064 18. JCommentsFactory::getACL() /var/www/astarmathsandphysics/components/com_jcomments/jcomments.php:188 0.3538 13858464 19. spl_autoload_call() /var/www/astarmathsandphysics/components/com_jcomments/classes/factory.php:274 0.3539 13858544 20. JLoader::load() /var/www/astarmathsandphysics/components/com_jcomments/classes/factory.php:274

Proof That the Rational Numbers With the Euclidean Topology is Totally Disconnected

Theorem

The set of rational numberswith the Euclidean topology is totally disconnected.

Proof

Letand let

An irrational numberexists satisfying

Define setsandby

andsois totally disconnected.

Add comment

Security code
Refresh