Cantor Confusion
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From: Franziska Neugebauer on 9 Dec 2006 06:14 mueckenh(a)rz.fh-augsburg.de wrote: > Franziska Neugebauer schrieb: [...] >> Provide one [definition of number]. Don't forget to provide a >> definition of "not-fixed" >> number and "not-fixed" set. And please show that one gains advantage >> over the function concept. >> > A function is a set of ordered pairs and as such it is not variable. True. > The expression "variable" is merely a relict from ancient times when > people knew that the objects of mathematics do not exist in some > nirvana but have to be present in a mind where not everything can be > present simultaneously. Let me summarize: 1. You do not present a convincing definition of "number". (Most likely you have none). 2. You do not present a convincing definition of "numbers" and "sets" which are "not fixed" or "un-fixed". 3. You do again try to discuss issues of neuro sciences (representation of abstract entities in mind (or in the brain?)) in sci math. F. N. -- xyz
From: Franziska Neugebauer on 9 Dec 2006 06:15 mueckenh(a)rz.fh-augsburg.de wrote: > > William Hughes schrieb: > > >> Recall this post from Dec 1 >> >> We extend this to potentially infinite sets: >> >> A function from the potentially infinite set A to the >> potentially infinite set B is a potentially infinite set of >> ordered pairs (a,b) such that a is an element of A and b is >> an element of B. > > A function, according to modern mathematics, is a set, actually fixed > and complete. The expression "variable" is merely a relict from > ancient times when people knew that the objects of mathematics do not > exist in some nirvana but have to be present in a mind where not > everything can be present simultaneously. copy-and-paste? >> We can now define bijections on potentially infinite sets > > Only if we consider them being actually infinite. But that would > exclude them from being potentially infinite. > > Regards, WM F. N. -- xyz
From: Bob Kolker on 9 Dec 2006 06:16 David Marcus wrote: > > Nonsense. If you use a word, you must define it. Please define > "countable number". Not every word can be (verbally) defined. This would lead to circularity. Some words can only be defined by ostention or example. Bob Kolker
From: Franziska Neugebauer on 9 Dec 2006 06:20 mueckenh(a)rz.fh-augsburg.de wrote: > Dik T. Winter schrieb: [...] >> Again you have provided neither a definition of "number", nor of >> "grow". >> Are you unable to do so? In common parlance, but that is not >> mathematics. In mathematics functions can grow in relation to their >> argument, but not the entities they denote. > > Functions cannot grow, according to modern mathematics. Wrong. I have provided a definition: ,----[ <45742128$0$97220$892e7fe2(a)authen.yellow.readfreenews.net> ] | Definition: A function f: A |-> B grows iff there exist a1 < a2 of | dom(f) and f(a1) < f(a2). We use the abbreviation "f grows" for of | "the function f grows". `---- > The expression > "variable" is merely a relict from ancient times when people knew that > the objects of mathematics do not exist in some nirvana but have to be > present in a mind where not everything can be present simultaneously. How do you call "Textbaustein" in English? F. N. -- xyz
From: Franziska Neugebauer on 9 Dec 2006 06:46
Bob Kolker wrote: > David Marcus wrote: >> >> Nonsense. If you use a word, you must define it. Please define >> "countable number". > > Not every word can be (verbally) defined. This would lead to > circularity. Some words can only be defined by ostention or example. EB's claim ,----[ <4579AE2A.4080001(a)et.uni-magdeburg.de> ] | Countability is self explaining. `---- is anemic: He neither defines nor explains what "Countablility" (of numbers) means. F. N. -- xyz |