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seen Sep 12 at 14:29

web design enthusiast and avid mathematics student


Jul
2
awarded  Curious
Apr
26
accepted Is every invertible matrix over an algebraically closed field diagonalisable?
Apr
23
answered Is every invertible matrix over an algebraically closed field diagonalisable?
Apr
23
comment Is every invertible matrix over an algebraically closed field diagonalisable?
Then I'll just refer to your comment, to close this thread–if you feel like it, you can still post one and of course I'll accept yours then.
Apr
23
comment Is every invertible matrix over an algebraically closed field diagonalisable?
Thanks a lot! Do you want to post your comment as an answer, so I can mark this question as answered?
Apr
23
comment Is every invertible matrix over an algebraically closed field diagonalisable?
I see my error in reasoning now: I still had orthogonal matrices in mind and the fact that they consist of rotations and mirroring(?)... thanks for clarifying!
Apr
23
asked Is every invertible matrix over an algebraically closed field diagonalisable?
Mar
31
comment Soft question: Examples where implications derived from mathematical models failed to describe reality
Zeno's paradox seems to be a falsidical one (sticking to Quine's classification); guess I've just been looking for antinomies (like Russel's), as their reasoning is correct, but their implications are "kind of false" (contradictory).
Mar
31
comment Soft question: Examples where implications derived from mathematical models failed to describe reality
@Jared: That's a pleasant point of view, however: Is there an objective criterion that distinguishes the "common", emergent axiomatic systems from others except that it seems to "fit reality"? (I guess the devil is in the details here, as 1+1=2 seems intuitively clear, but there are several ways to define a system in which this (and other basic assumptions) hold true)
Mar
30
comment Soft question: Examples where implications derived from mathematical models failed to describe reality
@DanielV: did Churchill also do mathematics or is this a joke? ~.^ Apart from that: thanks for the hint to paradoxes, still wondering why I didn't think of those before...
Mar
30
comment Soft question: Examples where implications derived from mathematical models failed to describe reality
@Jared: this fact that our axiomatic system is not just one of those "strange ones", but really seems to match reality is what fascinates me and my question was if this really is always the case (in particular whether there are specific counterexamples of theories that are sound and valid, but do not yield results relevant to real world)
Mar
28
comment Soft question: Examples where implications derived from mathematical models failed to describe reality
Also: If premises are correct (and your argument is valid), does this also mean every conclusion (in particular every proof within the system) may be applied to reality as well? Theoretically I could define an axiomatic system with another multiplication and feed it with some "perfectly accurate" and sound real world data, make some proofs, but most likely the proven results will not have anything to do with reality anymore.
Mar
28
comment Soft question: Examples where implications derived from mathematical models failed to describe reality
If you could elaborate on why this question is pointless, this would be an answer as well I guess - to be honest I'm not feeling overly proficient here :) The problem you are addressing in the last paragraph pretty much sums up my amazement that theories can describe reality so well and even lead to progression and as there are so many examples where it "just works" nonetheless, I was wondering if there are counterexamples as well.
Mar
28
comment Soft question: Examples where implications derived from mathematical models failed to describe reality
I have a hard time being able to relate to this - if premises are correct, then the conclusions are correct within the formal system we are working in, but not necessarily for "reality". (I edited the original question accordingly) (I hope geodude is not sore, but I am answering to this point here, as it is hard to keep track of a discussion going on in the original question's comment section)
Mar
28
revised Soft question: Examples where implications derived from mathematical models failed to describe reality
clarification II
Mar
28
revised Soft question: Examples where implications derived from mathematical models failed to describe reality
clarification
Mar
28
revised Soft question: Examples where implications derived from mathematical models failed to describe reality
added 2 characters in body
Mar
28
asked Soft question: Examples where implications derived from mathematical models failed to describe reality
Oct
27
accepted Lebesgue measure vs. Borel measure
Oct
27
comment Lebesgue measure vs. Borel measure
analysis.math.uni-kiel.de/schuett/masstheo.pdf (danger: German) on site 58 (point III), but dumb me just realized that this only holds true for sets whose measure is > 0...