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visits member for 2 years, 4 months
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web design enthusiast and avid mathematics student


Sep
24
awarded  Autobiographer
Sep
21
comment What can I think of the function $F$ that's being used for most(?) explicit first order ODEs?
@"Are there any such sentences in the book? Did the professor say anything at all while writing those formulas?" There aren't any explanations in the book and I couldn't attend the lecture (as well as multivariate calculus which might explain the above problem) because I had to do alternative service. Maybe he said something in the lectures, but my fellow students didn't have a clue either.
Sep
21
comment What can I think of the function $F$ that's being used for most(?) explicit first order ODEs?
Thank you very much! Finally I have an idea of what $F$ looks like! The last equation makes perfectly sense now and the second last the problem reduced to the question why there's an $F$ after $\frac{\Delta F}{\Delta y}$ and not after $\frac{\Delta F}{\Delta t}$, but I guess this has something to do with $y$ being a vector. However, this is not part of the original question anymore.
Sep
21
accepted What can I think of the function $F$ that's being used for most(?) explicit first order ODEs?
Sep
20
comment What can I think of the function $F$ that's being used for most(?) explicit first order ODEs?
That still leaves me without a clue what the last term (and others) means though, isn't there any intuitive explanation what the single arguments are for?
Sep
20
asked What can I think of the function $F$ that's being used for most(?) explicit first order ODEs?
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)