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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!
Jul
14
comment Can the indexing set of a cartesian product have the cardinality of the continuum?
I suggest you take a look at en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
Jul
14
comment Can the indexing set of a cartesian product have the cardinality of the continuum?
@Manos: great question. How do you know it? Axioms! For example, $\mathbb{N}$ is a set (axiom of infinity). Also, the power set of any set is a set (axiom of power set). A subset of a set is a set (axiom of comprehension). The range of a function is a set (axiom of replacement). (I'm being deliberately non-formal). You can prove from the usual axioms of ZF that $\emptyset$ is a set. So, we know there are some things which are sets by axioms, and then we know how to build more sets from them, by axioms which allow us some constructions.
Jul
14
revised Can the indexing set of a cartesian product have the cardinality of the continuum?
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