I was using my knowledge of Jungian and the MMPI which are the most widely used and thus easiest to draw inferences from. — SkyLeach
I'm generalizing and try never to use them to evaluate any individuals — SkyLeach
Academics is, at its core, an appeal to authority. — SkyLeach
Mathematics is what a consensus of mathematicians says it is. — jgill
is an uncountable infinity a mathematical object? — Agent Smith
But as to whether a purported proof is correct or not (unless it is extraordinarily complicated) is not a matter of consensus — TonesInDeepFreeze
Whatever consensus there might be, if one shows an incorrect inference in a purported proof, then the proof is disqualified from being deemed an actual proof. — TonesInDeepFreeze
I meant to ask was whether something uncountable (an example of an uncountable infinity is the set of real numbers R) can be considered mathematical? — Agent Smith
After all, math is, bottom line, about countability (0, 1, 2, 3,...). — Agent Smith
It's still a matter of consensus to determine whether the proof is valid. — jgill
humans have to agree before it becomes an accepted piece of mathematics — jgill
Whatever consensus there might be, if one shows an incorrect inference in a purported proof, then the proof is disqualified from being deemed an actual proof.
— TonesInDeepFreeze
Guess there's not a consensus, then. — jgill
That doesn't entail that mathematics must be limited to the natural numbers. — TonesInDeepFreeze
Yes, it is a mathematical object. — ssu
Counting lies at the heart of mathematics. An uncountable object (e.g. the set of reals), therefore, must be, in some way, nonmathematical, oui? — Agent Smith
You didn't ask — SkyLeach
↪SkyLeach
I'm somehow not convinced by your words. Uncountability is, in a sense, beyond (conventional) mathematics seen as a counting activity.
True that the variety of numbers has expanded over history. Yet we seem distinctly more comfortable with the category of natural numbers than with any other I can think of. — Agent Smith
Any set can be defined as a vector — SkyLeach
There is too much direct control asserted over too much of each generation's career by the previous generation, causing the normal evolution of thought and culture to be retarded in academics — SkyLeach
Any set can be defined in terms of its periodicity function — SkyLeach
Oh my god! You discovered the hidden truth that there is a rupture in mathematics! Division is not closed in the integers! A discovery as shocking as that Soylent Green is people! And there is not just your example, but thousands of them! Millions of them! Maybe even infinitely many of them! And this contagion is not confined just to mathematics but it affects even the entire garment industry! — TonesInDeepFreeze
Do you mean differentiable manifolds? A cylinder created by moving a circle through space is not curved? A sphere in 3-D is not composed of points? — jgill
The sequence <2,7,9> can be seen as a vector. The set {2,7,9} cannot, since the positions of the elements is arbitrary — jgill
What's that? So a set of random integers is defined that way? Do you speak of a set or a sequence? — jgill
Not my experience — jgill
A sphere in 3-D is not composed of points? — jgill
Nope, I definitely haven't done whatever you said. I also have no clue how to do that because I don't understand. — SkyLeach
How can something that can't be counted be mathematical? — Agent Smith
How can something that can't be counted be mathematical? Can consciousness be counted? — Agent Smith
Set theory isn't just sets of points, it can also be a scene described as a space (hilbert, sobolev, etc...) with objects described functionally instead of sets of points. I deal far more with scenes described rather than sets of points except when rendering a solution set. — SkyLeach
When I talk about many of the problems in academia I tend to be thinking of cosmology, astronomy, paleontology, the humanities (psych, anthro, socio, etc...) The more empirical and rigid a discipline is the less they seem to get into academic problems — SkyLeach
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