My Math Forum  

Go Back   My Math Forum > Math Forums > Math Books

Math Books Math Book Forum - Math books, ebooks, references

Thanks Tree1Thanks
  • 1 Post By Maschke
LinkBack Thread Tools Display Modes
September 28th, 2018, 02:05 PM   #1
Joined: Sep 2018
From: Poland

Posts: 3
Thanks: 0

Question Do you have F. Waismann's: Intro. to Mathematical Thinking

Friedrich Waismann: Introduction to Mathematical Thinking. The Formation of Concepts in Modern Mathematics. (14. Ultrareal numbers)
If you have it, would you be so kind as to quote what it states about
ultrareal numbers?
My email:
htg is offline  
September 28th, 2018, 07:22 PM   #2
Senior Member
Joined: Aug 2012

Posts: 2,355
Thanks: 737

Can't help with the book but found a reference on nLab.

where each operation is defined by iterating the previous one (the next operation in the sequence is pentation). The peculiarity of the tetration among these operations is that the first three (addition, multiplication and exponentiation) are generalized for complex values of n, while for tetration, no such regular generalization is yet established; and tetration is not considered an elementary function. Addition (a + n) is the most basic operation, multiplication (an) is also a primary operation, though for natural numbers it can be thought of as a chained addition involving n numbers a, and exponentiation (an) can be thought of as a chained multiplication involving n numbers a. Analogously, tetration (na) can be thought of as a chained power involving n numbers a. The parameter a may be called the base-parameter in the following, while the parameter n in the following may be called the height-parameter (which is integral in the first approach but may be generalized to fractional, real and complex heights.

So it's essentially about abstract tetration. nLab is a site devoted to n-categories so I'm pretty sure that it's tetration on steroids.

OP is this definition of ultrareal numbers the same or different as the usage in the book?
Thanks from ProofOfALifetime
Maschke is online now  
September 28th, 2018, 09:53 PM   #3
Math Team
Joined: Dec 2013
From: Colombia

Posts: 7,674
Thanks: 2654

Math Focus: Mainly analysis and algebra
It's not complete, but:
v8archie is offline  

  My Math Forum > Math Forums > Math Books

intro, mathematical, thinking, waismann

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Ultrareal numbers (in Friedrich Waismann's book) htg Number Theory 0 September 28th, 2018 11:48 AM
Thinking Theta New Users 21 August 6th, 2014 05:26 PM
Mathematical Thinking: 2 Derangements/proof questions zukias Applied Math 0 December 10th, 2010 02:41 PM

Copyright © 2019 My Math Forum. All rights reserved.