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 361992 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.0534 1210640 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.0534 1210640 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.1462 4038112 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.1476 4065664 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.1484 4083376 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.1484 4100384 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.1491 4108120 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.1491 4108120 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.2124 4335040 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.2140 4352440 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.2146 4373368 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.2248 4438192 13. Joomla\CMS\Plugin\PluginHelper::importPlugin() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:189 0.2248 4438448 14. Joomla\CMS\Plugin\PluginHelper::import() /var/www/astarmathsandphysics/libraries/src/Plugin/PluginHelper.php:182

The Problem With Infinity

Infinities don't behave like proper numbers. It makes sense to write  
\[x--x=0\]
  when  
\[x\]
  is an ordinary number but not when  
\[x\]
  is infinity. This is because when  
\[x\]
  is multiplied by 2 the result is  
\[2x\]
  but when infinity is infinity is multiplied by infinity, the result is infinity.
Because of this following proof contains an error.
\[S=1++2+4+8+16+32+...+ \infty +...\]
(1)
\[2S=2+4+8+16+32+...+ \infty +...\]
(2)
(2)-(1) gives
\[S=-1\]
. This is obviously wring since all terms rare positive. The above technique will only work if  
\[\frac{a_{n+1}}{a_n} =r<1\]
  for  
\[n=1,2,3,...\]
 

Add comment

Security code
Refresh