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 September 28th, 2018, 02:05 PM #1 Newbie   Joined: Sep 2018 From: Poland Posts: 3 Thanks: 0 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@interia.pl
 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. https://ncatlab.org/nlab/show/ultrareal+numbers 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
 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: https://books.google.com.co/books?id...umbers&f=false

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