My Math Forum  

Go Back   My Math Forum > High School Math Forum > Pre-Calculus

Pre-Calculus Pre-Calculus Math Forum


Thanks Tree4Thanks
Reply
 
LinkBack Thread Tools Display Modes
January 14th, 2016, 04:09 PM   #11
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,655
Thanks: 2633

Math Focus: Mainly analysis and algebra
Oh yes, I agree with that. My main problem with the hyperreals is that they don't seem to add any value. The only "benefit" I recall hearing about being that they can make calculus accessible to people who don't understand limits. To which my response is: well teach them limits in a clearer fashion then! Or, don't bother teaching the rigorous foundations at all.
Thanks from Maschke
v8archie is offline  
 
February 23rd, 2016, 04:57 AM   #12
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 3,264
Thanks: 902

It has a historical value- When Sir Isaac Newton developed the Calculus, he used 'infinitesmals' without properly defining them. Hyperreal numbers allow one to rigorously define those 'infinitesmals'.
Country Boy is offline  
February 23rd, 2016, 06:44 AM   #13
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,655
Thanks: 2633

Math Focus: Mainly analysis and algebra
Indeed so (and Leibnitz used them too). Infinitesimals show that their intuition that infinitesimals could be used to penetrate the subject was well founded. But unfortunately the modern theory retains the core objection to those infinitesimals by validating the idea that you just ignore them when you are ready to transport your result to the reals. It's all perfectly rigorous but just as unsatisfying now as it was 300 years ago.
Thanks from Country Boy
v8archie is offline  
Reply

  My Math Forum > High School Math Forum > Pre-Calculus

Tags
difference, hyperreal, numbers, real



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Proof difference of two natural numbers godingly Calculus 0 November 4th, 2014 10:06 AM
First proof! - The difference of two numbers is scalable ryanninjasheep Applied Math 1 February 28th, 2014 03:55 PM
Difference between real analytic and holomorph? ChidoriPOWAA Complex Analysis 2 April 2nd, 2013 11:58 PM
Prove the difference between numbers stevecowall Algebra 1 March 27th, 2012 06:47 PM
Find two numbers where difference is 20 & the sum is -4 sharp Elementary Math 7 October 30th, 2010 08:52 AM





Copyright © 2019 My Math Forum. All rights reserved.