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Jul
26
awarded  Nice Question
Jul
20
comment Reference request: is mathematics discovered or created?
FWIW, I ended up writing the essay on something else (also math-related, though); so for those who were reluctant to throw out some ideas, be at ease: the answers and comments "only" contributed to my knowledge of these profoundly interesting matters.
Jul
19
comment Interpretation of a formula and truth
@Kaveh: thank you for your comments, I think I understand this better now.
Jul
18
comment Interpretation of a formula and truth
I understand. Still, I'm not fully convinced of why this is meaningful.
Jul
18
comment A simple question about sine and cosine
$sin(z)= \frac{e^{iz}-e^{-iz}}{2i}$ for complex $z$ is the first that comes to mind. There are others, see en.wikipedia.org/wiki/Sine for a continued fraction expression for example. Also, I remember Apostol defining sine and cosine in his Calculus by some fundamental properties...
Jul
18
revised Interpretation of a formula and truth
edited tags
Jul
17
comment Interpretation of a formula and truth
@André: But if in the end I just have to think as $\mathbb{N}$ as something "intuitive" and $0\cdot n=0$ as an intuitive truth, why then care for any formalism at all?
Jul
17
comment Interpretation of a formula and truth
@Zev: great, thanks! This is a bug that should be reported, actually.
Jul
17
accepted Models of hyperbolic geometry
Jul
17
accepted Reference request: is mathematics discovered or created?
Jul
17
comment Interpretation of a formula and truth
There's some funky latex going on there, I don't know why that is happening.
Jul
17
asked Interpretation of a formula and truth
Jul
17
comment Evaluating matrix-continued fractions?
Why not ask on MathOverflow?
Jul
16
comment Why some people don't like proofs by contradiction
I don't think I can give a good answer; while you wait for one, you should see read on intuitionistic logic (en.wikipedia.org/wiki/Intuitionistic_logic)
Jul
16
comment Solving $\lim\limits_{x \to 0^+} \frac{\ln[\cos(x)]}{x}$
@Javier: Exactly! You try to see your limit as the derivative of a function on a given point. Once you got it that way, you calculate the derivative of the recognized function using standard methods, evaluate it on the point, and voilà.
Jul
16
comment Solving $\lim\limits_{x \to 0^+} \frac{\ln[\cos(x)]}{x}$
@Javier: what's the definition of the derivative?
Jul
15
awarded  Nice Answer
Jul
15
awarded  Enlightened
Jul
15
comment What does “a map is isomorphic to another map” mean?
@Qiaochu: why can't/don't they introduce the xymatrix package to the SE network?
Jul
14
comment Can the indexing set of a cartesian product have the cardinality of the continuum?
@Theo: thank you!