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bio website von-eitzen.de/math/tntrep.xml
location Bonn, Germany
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I did study math and had a knack for it, but I am sooo out of that business now ...

comment Example of dependent but conditional independent
$P(Y)=P(Z)=\frac12$, but $P(Y,Z)=\frac12\cdot \frac34\cdot\frac34+\frac12\cdot\frac14\cdot\frac14=\frac5{16}\ne\frac14$.
comment Lower bound of the index of a subgroup of a non abelian simple group
You mean proper subgroup.
comment Need to negate this proposition!
The "and" between quantors better viewed as a "such that".
comment A and B are sets. Prove that A=B iff P(A) = P(B) where P is the power set.
Just note that $\bigcup P(A)=A$.
comment How to get a number that is divisible by $n$ - without obviously seeing it?
@user2345215 D'oh, if you want to read a recipe that enforces divisibility, your mind simply ignores such crucial words. :) - Jsut like sentnces with lots of msipselld words are stlil more or less raedable ...
comment sub-algebra of continuous real valued functions without unit must vanish at a point
Don't we need proper subalgebra?
comment How to get a number that is divisible by $n$ - without obviously seeing it?
Well, let's see. Think of a three-digit number, but not ending in zero or five and digit sum not a multiple of three. Now take it to the eighth power and subtract one. I magically foresee that the result is divisible by fifteen. - Your audience won't like you.
comment Solve an Angle-Side-Angle special case triangle if it has an obtuse angle?
Why dont you try the law of sines? It works.
comment Compact sets of real number
Can you use that a continuous function on a compact set attains its minimum? Or that the product of compact spaces is compact?
comment Insights in solving systems of eqn?
The for the moment forget about $I_3AI_4$, whatever that is. Try to obtain new - simpler - equations by adding / subtracting known equations. For example, add the first and third to immediately see what $x_3$ must be ...
comment In how many ways can i build this String : abbcccdddd?
As it seems, there is only one way :)
comment Dual Vector Space embedding
In the first line you ask for an embedding, in the last line for a natural embedding. These are different questions (and have different answers).
comment Logarithm of a negative number
Nothing. You dropped the condition "whenever $a,b>0$" from the full steatement of the identity.
comment When do eigenvectors converge?
If $\{v_n\}_{n\in\mathbb N}$ is a sequence such that $A_nv_n=\lambda v_n$, it is not necessarily the case that $v_n$ converges in the first place. Think of $A=A_n=I$, $\lambda=\lambda_n=1$ for all $n$ and $v_n$ some "random" sequence.
comment Please give feedback to this solution.
The "closed as duplicate" is possibly not fully justified. The duplicate asks whether we can conclude that $n$ is prime if it has no divisor $<10^6$ (and we have $n\gg 10^{12}$); the answer is of course "no". This question aks the same if it is known that $n$ has no prime divisor $<n-10^6$; here the answer is "yes" as soon as $n>1001001$, say). - The fact that the actual $n\gg10^6$ chosen can be explicitly factored doesn't touch the question as such.
comment Every integer greater than 1 is divisible by at least one prime. Can anyone please express this in logical notation
Do you have predicates for "is integer", "is greater than", "divides", "is prime" and a constant symbol for "1" available?
comment Exercises in combinatorics
Where do cycles come from in 3)?
comment Irrationality of $\pi$ and circumference to diameter ratio.
Note that $\frac13$ also has "never ending numbers after decimal". This doesn't contradict the fact that $\frac13$ is finite.
comment exercise involving exactness
I assume here monomorphism only means left-cancelable?
comment prove that commuting ring is a subring of E(M) .
$E(M)$ is a ring with pointwise addition as addition and composition as multiplication. But that is in general not commutative.