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Sep
26
comment Is infinite a infinite or finite
Quite the opposite: Cantor showed that there's not only one infinity, but infinitely many.
Sep
26
comment 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.
Sep
25
comment 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.
Sep
25
comment What are imaginary numbers?
@MakotoKato: I didn't say it is. I applied your argument to language, to demonstrate that it doesn't work.
Sep
25
comment 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?
Sep
24
revised Find all $a$ such that $\{x_n\}$ has finite limit
\[ and \] replaced by $$
Sep
24
comment 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.
Sep
24
comment Isn't this a problem when evaluating the auxiliary equation?
What exactly did you enter in Wolfram Alpha? Because I get "$0$ assuming $\alpha>0$"
Sep
24
answered What is the difference between an array and a vector?
Sep
23
comment Proof: If n is a perfect square, $\,n+2\,$ is NOT a perfect square
That proof only works for $n>0$ (but for $n=0$ it's easily checked directly).
Sep
23
revised Some quick math problems I'm stuck on
fixed a mistake in the explanation
Sep
23
comment Is probability objective?
Well, the last case would be for example if Bob eats the white ball twice as often as the black ball, the probability of the box containing the white ball is $1/3$, which is neither $0.5$ nor $0$ nor $1$. And yes, people disagree about the correct interpretation of probabilities.
Sep
23
answered Some quick math problems I'm stuck on
Sep
23
comment Is probability objective?
If you are a Bayesianist, both are right. If you are a frequentist, it depends on whether, when repeating the experiment many times, Bob would choose the same ball each time (then Bob is right), would choose each ball equally often (then Alice is right), or would only show a certain bias for one color (then neither is right).
Sep
23
revised What is the meaning of $P(A \cup B)$ in probability and statistics?
added 167 characters in body
Sep
23
answered What is the meaning of $P(A \cup B)$ in probability and statistics?
Sep
23
comment confusion over the use of universes in category theory
And I fixed the even i. :-)
Sep
23
revised confusion over the use of universes in category theory
fixed another i
Sep
22
awarded  Nice Question
Sep
22
comment Selection through identical balls
Unless you are doing quantum mechanics, "identical" things don't exist.