Deprecated: Constant E_STRICT is deprecated in /home/polpe/public_html/system/core/Exceptions.php on line 75

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_URI::$config is deprecated

Filename: core/URI.php

Line Number: 101

Backtrace:

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Router::$uri is deprecated

Filename: core/Router.php

Line Number: 127

Backtrace:

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$benchmark is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$hooks is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$config is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$log is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$utf8 is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$uri is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$exceptions is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$router is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$output is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$security is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$input is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$lang is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$load is deprecated

Filename: core/Controller.php

Line Number: 78

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$parser is deprecated

Filename: core/Loader.php

Line Number: 1290

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$form_validation is deprecated

Filename: core/Loader.php

Line Number: 1290

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$MyModel is deprecated

Filename: core/Loader.php

Line Number: 353

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 282

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 17
Function: library

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: session_set_cookie_params(): Session cookie parameters cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 289

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 17
Function: library

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 304

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 17
Function: library

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 314

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 17
Function: library

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 315

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 17
Function: library

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 316

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 17
Function: library

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 317

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 17
Function: library

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: drivers/Session_files_driver.php

Line Number: 94

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 17
Function: library

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: session_set_save_handler(): Session save handler cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 108

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 17
Function: library

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: session_start(): Session cannot be started after headers have already been sent

Filename: Session/Session.php

Line Number: 141

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 17
Function: library

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$session is deprecated

Filename: core/Loader.php

Line Number: 1290

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 17
Function: library

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$benchmark is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$hooks is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$config is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$log is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$utf8 is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$uri is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$exceptions is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$router is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$output is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$security is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$input is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$lang is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$load is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$parser is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$form_validation is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$MyModel is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$session is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

Polcz Péter honlapja

Tartalomjegyzék

Matematikai indukció

TELJES MATLAB SCRIPT KIEGÉSZÍTŐ FÜGGVÉNYEKKEL

file:   d2017_09_17_indukcio.m
author: Peter Polcz <ppolcz@gmail.com>
Created on 2017. September 17.
Output:
┌d2017_09_17_indukcio
│   - Persistence for `d2017_09_17_indukcio` initialized [run ID: 1321, 2017.09.17. Sunday, 13:37:50]
│   - Script `d2017_09_17_indukcio` backuped

Faktoriálisos feladat

$$ \prod_{i = 1}^n (2 k)! < [(n+1)!]^n $$

n = 10;
for i = 1:n
    faktorialisok = cumprod(1:2*n);
    baloldal = prod(faktorialisok(2:2:2*n));
    jobboldal = factorial(n+1)^n;

    if baloldal < jobboldal
        disp 'baloldal < jobboldal';
    elseif baloldal == jobboldal
        disp 'baloldal = jobboldal';
    else
        disp 'baloldal > jobboldal';
    end
end
Output:
baloldal > jobboldal
baloldal > jobboldal
baloldal > jobboldal
baloldal > jobboldal
baloldal > jobboldal
baloldal > jobboldal
baloldal > jobboldal
baloldal > jobboldal
baloldal > jobboldal
baloldal > jobboldal

End of the script.

Output:
└ 0.080151 [sec]