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19h
revised taylor series of ln(1+x)?
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19h
answered taylor series of ln(1+x)?
21h
comment Does adding linearly independent vectors retain linear independence?
Note that if the underlying field has characteristic $2$, we have linear dependence.
22h
comment What is the reason for the one-half in the normal pdf's gaussian (i.e. : why $\exp(-x^{2}/2)$ instead of $\exp(-x^{2})$ )
You are welcome. There are quite a few distributions for which a normalized version essentially tells the whole story. For example the general exponential with density function $\lambda e^{-\lambda x}$ is just a scaled version of the normalized exponential with density function $e^{-x}$.
22h
comment What is the reason for the one-half in the normal pdf's gaussian (i.e. : why $\exp(-x^{2}/2)$ instead of $\exp(-x^{2})$ )
Certainly the integral is $1$. But in my answer I said the purpose of the $1/2$ is to make the variance $1$. Choosing $e^{-x^2}$ makes the variance equal to $1/2$.
22h
comment Find whether the following series converges or diverges $\sum_{n=1}^{\infty}\frac{\ln n }{\sqrt{n}}$
AST does not apply, no alternation in sign. We have divergence.
22h
comment Why do some universities offer mathematical logic in different departments?
Sometimes there are people in logic in both departments, and sometimes they even talk with each other. Programs are usually not similar in their content. At the many universities that have qualifying exams, these will be entirely different in content.
22h
answered What is the reason for the one-half in the normal pdf's gaussian (i.e. : why $\exp(-x^{2}/2)$ instead of $\exp(-x^{2})$ )
23h
comment In 30 boxes are 15 balls. Chance all balls in 10 or less boxes?
There is no good reason to use a probability model in which all partitions are equally likely. A more natural model has us throwing the balls one at a time, with all $30$ boxes equally likely.
23h
comment Will I will be able to sit and watch the movie?
The analysis would be very difficult. Assume couples. If they choose adjacent seats at random, there will be usually many gaps of $1$, and $3$ in a row has very low probability. But one could at best hope for estimates.
1d
comment Will I will be able to sit and watch the movie?
The last condition may make the problem too difficult to solve except by a simulation. The condition is also somewhat unspecific. Does it mean people come in couples?
1d
comment Elementary equivalence of models
You are welcome. It is a standard term in model theory, not to be confused with the Completeness Theorem. A theory $T$ is complete if for any sentence $\phi$ one of $\phi$ or $\lnot\phi$ is a theorem of $T$. The theory $\mathcal{T}(\mathfrak{A})$ is complete because a sentence is either true or false in $\mathfrak{A}$. A more interesting example of a complete theory is the theory of algebraically closed fields of characteristic $0$. Also the theory of real-closed fields.
1d
answered Elementary equivalence of models
1d
awarded  Enlightened
1d
comment mathematical modeling
Very salty liquid! Liquid at time $t$ (for a while) $200+4t$. If $A(t)$ is the amount of salt at time $t$, we have rate IN: easy. Rate OUT: $12 \frac{A(t)}{200+4t}$.
1d
awarded  Nice Answer
1d
comment Solve for $x$: $\frac1e = e^{2x}$
If the question really is reported correctly, and you are looking for the real solution, $x=-1/2$ is right.
1d
comment Find $\tan x $ if $\sin x+\cos x=\frac12$
If you knew $\cos x$, say, you would probably be fine. So you could write $\sin x=1/2 -\cos x$ and square both sides.
1d
answered Is it true that if $f'(x) > g'(x)$ then $f(x) >g(x)$?
1d
comment If algebraic $a$ has degree $n$, so does $-a$
You are welcome. Above, I was kind of sloppy, should have said a minimal polynomial. Multiplying a minimal polynomial by a non-zero constant gives another minimal polynomial.