My Math Forum  

Go Back   My Math Forum > High School Math Forum > Elementary Math

Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

LinkBack Thread Tools Display Modes
July 6th, 2018, 02:11 AM   #1
Senior Member
Joined: Dec 2015
From: Earth

Posts: 232
Thanks: 26

Inverse Logic

From A we solve B or $\displaystyle A\rightarrow B$
By inverse we get $\displaystyle B\rightarrow A \rightarrow A\equiv B$
Let's use it to solve equations below:
Given equation $\displaystyle a(x)=b(x)$we transform to $\displaystyle a(x)-b(x)=0$ or $\displaystyle z(t)=0$
From $\displaystyle \frac{dz}{dt} =0 $ we find extremum of $\displaystyle z(t)$ (if it exist ofc)
Now by inverse theory we find value $\displaystyle t_0$ for which $\displaystyle \int z(t)dt=E[\int z(t)dt]$ so now we have an
equivalence $\displaystyle \frac{dz}{dt}=0 \equiv \min\{ \int z(t)dt \}=\int z(t)dt$
Let's take a great example below:
Given equation $\displaystyle x=\sin x$ we transform to $\displaystyle x-\sin x =0$ now if value $\displaystyle x_0 $ satisfies the equation $\displaystyle \frac{1}{2} x^2 +\cos x = \min( \frac{1}{2} x^2+\cos x )$
then $\displaystyle x_0 $ holds for $\displaystyle x_0=\sin x_0$
For those who further info, I have solved equations with this method like below:
$\displaystyle e^x=x+1$ , $\displaystyle e^x=ex$ , $\displaystyle a^x=x+1 ...$ etc

Last edited by skipjack; July 6th, 2018 at 06:07 AM.
idontknow is offline  
July 6th, 2018, 02:36 AM   #2
Senior Member
Joined: Oct 2009

Posts: 430
Thanks: 144

Yes, root finding problems and minimization problems are closely related. So what is your point?
Micrm@ss is offline  

  My Math Forum > High School Math Forum > Elementary Math

inverse, logic

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
prove logic equation, logic algebra dmnte Computer Science 0 April 23rd, 2015 10:45 PM
Logic KyVanchhay Math Events 1 July 31st, 2013 01:51 AM
Logic orokusaki Applied Math 4 April 4th, 2012 05:03 AM
find inverse of inverse function jaredbeach Algebra 1 November 17th, 2011 11:58 AM
right inverse and left inverse JOANA Abstract Algebra 0 March 18th, 2011 06:29 AM

Copyright © 2018 My Math Forum. All rights reserved.