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| bio | website | |
|---|---|---|
| location | ||
| age | 41 | |
| visits | member for | 10 months |
| seen | Oct 26 '12 at 6:50 | |
| stats | profile views | 260 |
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Sep 30 |
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Is this a Dedekind's cut? Hint: What if $r$ is rational? |
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Sep 30 |
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Proving statement about dimensions of vector spaces You mean $\dim S+T$. $S\cup T$ will in general not be a subspace. |
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Sep 30 |
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Proving statement about dimensions of vector spaces The other relation you need is that the dimensions of kernel and image add up to the dimension of the domain. |
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Sep 30 |
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Axiom of Regularity @MartinSleziak: With the standard construction of the natural numbers, no element of this set is a subset, because all of them contain the empty set, which is not an element of $A$. You probably meant $A=\{0,1,2,3,4,5\}$ |
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Sep 30 |
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Prove identity involving powers and trigonometric functions Hint: $\mathrm e^{\mathrm i\phi}=\cos\phi + \mathrm i\sin\phi$ |
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Sep 30 |
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Prove identity involving powers and trigonometric functions sin → \sin, cos → \cos, prooving → proving |
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Sep 30 |
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Is the set of all valid C++ programs countably infinite? While on any given computer the memory is finite, you still can just build a bigger computer. Also, there is nothing in the C++ standard demanding that a valid C++ program must at some instance of time be stored completely on the computer. |
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Sep 30 |
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Is the set of all valid C++ programs countably infinite? C++ is not bound to a specific implementation. Every single implementation may (and will) have resource limits, that is, for any C++ implementation there will be a valid C++ program which cannot be handled by the given C++ implementation. So not being able to compile and/or execute a program on any given machine doesn't make it an invalid C++ program (nor the implementation of C++ a non-conforming implementation, as long as it documents its resource limits). Since C++ does not put any upper limit on the size of pointers, it also does not put a limit on the memory a C++ program can use. |
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Sep 30 |
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Locus perpendicular to a plane in $\mathcal{R}^4$ Your edit is fine, too. |
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Sep 30 |
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What are imaginary numbers? there are in nature any objects which indeed do have well-defined locations and momenta; indeed, according to quantum mechanics, they don't, and modern experiments agree with the quantum mechanica predictions). |
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Sep 30 |
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What are imaginary numbers? @MakotoKato: I'm a physicist working in quantum information, so I know quantum mechanics quite well. However, I'm also able to distinguish between the model of reality (Quantum mechanics) and reality itself. The success of quantum mechanics shows that there's something in nature which can be quite well mapped onto mathematical structures using complex numbers. That does not imply that there are complex numbers in nature (just as the fact that for centuries we've successfully mapped real objects onto locations and momenta which are exactly defined at the same time doesn't imply that … |
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Sep 26 |
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Locus perpendicular to a plane in $\mathcal{R}^4$ I cannot find an error. |
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Sep 26 |
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How do I cube/square a logarithm? Did you also copy the dollar signs, and did not prefix it with four spaces? |
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Sep 26 |
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Is infinite a infinite or finite Quite the opposite: Cantor showed that there's not only one infinity, but infinitely many. |
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Sep 26 |
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Difference between sq km and km sq The notation $4\,\mathrm{km}^2$ will be understood all over the world. The notation $4\,\mathrm{sq. km}$ only in English speaking countries. |
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Sep 25 |
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What are imaginary numbers? @MakotoKato: Your argument was using the rule: "X turns out to be very useful, if not essential, for theories of physics, therefore X is somehow part of the universe." You applied that argument for "X=mathematics". I applied it for "X=language" and got an obviously wrong result, thus invalidating the rule. Since the rule is invalid, its application to mathematics is also invalid. |
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Sep 25 |
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What are imaginary numbers? @MakotoKato: I didn't say it is. I applied your argument to language, to demonstrate that it doesn't work. |
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Sep 25 |
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What are imaginary numbers? @MakotoKato: To answer this question, let me ask another question: All theories are written in some language, be it Latin, English, German or whatever. Using a language turns out to be essential for writing theories; you couldn't do it without. Should I conclude that languages are not a construct of the human mind, but somehow part of the intrinsic structure of the universe? |
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Sep 24 |
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Find all $a$ such that $\{x_n\}$ has finite limit \[ and \] replaced by $$ |
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Sep 24 |
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Isn't this a problem when evaluating the auxiliary equation? @KorganRivera: Since I don't know the 2nd order differential equation you are trying to solve, or how this equation relates to it, I cannot say for sure, but I'd bet no. For any finite $x$ and finite $\alpha$, either the polynomial or $K$ must be $0$ in order to solve that equation. So unless a legitimate solution of the differential equation would correspond to infinite $x$ or infinite $\alpha$, there should not be a problem. |
