106,324 reputation
696194
bio website von-eitzen.de/math/tntrep.xml
location Bonn, Germany
age 48
visits member for 1 year, 10 months
seen 40 mins ago

I did study math and had a knack for it, but I am sooo out of that business now ...


1h
comment My proof of the recursion principle
I'm not very happy with "maximum element of domain". Why not use replacement to take the domain of $f$ itself? (This may require some special cases near $0$) Or do you already have $n^-$ on $\mathbb N\setminus\{0\}$ readily available?
3h
comment Calculate distance between two objects based on their visible height for a specific focal length
A focal length of 35mm means that a point at infinity is mapped to a point 35mm behind the lens. However if your 15cm object is mapped to an image of 12cm, i.e. almost its original size, we are talking about the lens moved considerably away from the image plane (namely approximately into the middle between image plane and object; we'd have exactly the middle if the image size were equal to the object size). At any rate, without additional information, only the relative distances of the objects from the lens can be inferred from the quotient of their sizes.
3h
comment Prove that intersection of connected spaces is connceted.
Let $A$ be the unit circle and $B$ the $x$-axis within the two-dimensional plane. Which of $A,B,A\cap B$ are conncted?
3h
comment Why does this graph only the positive side
Hint: Do you think that $\sqrt[4]{x^2}=x^{2/4}=x^{1/2}=\sqrt x$ for all real numbers $x$?
23h
comment Where's the problem with a false “proof”: $\;1^0 = 1^2 \overset{?}\implies 0 = 2$
Apparently it is. Otherwise, we'd have $0=2$.
1d
comment Does the boundaries of non-disjoint sets in Euclidean space have common element?
Well, you need to add a few conditions. For example if the sets are open, not disjoint, not contained in one another, and connected ...
1d
comment Primitive-recursive functions and polynomial equations
Unless $K(m,n)$ is constant, $\prod_{i=0}^{K(n,m)}(P(n,m,i)-Q(n,m,i))$ is not of the form $P(n,m)-Q(n,m)=0$.
1d
comment Proving some properties of $\Bbb N$ without using recursion
@Graduate I don't think that William wanted to object against referencing the axioms, but against referencing them by a local obscure notation. Saying Axiom of Infinity or simply INF instead of ZF7, Axiom of Power Set or simply POW instead of ZF4, Axiom Schema of Separation or simply SEP instead of ZF5 would have made a reference to the axioms as intended - and the reader would know which are meant.
1d
comment Pick a smart function
Is there a reason for the parentheses on the right hand side? Should there possibly be a $-\cos x$ in one of the two equations?
1d
comment Seminorm proof of a function
Just verify the defining conditions (which is straightforward)
1d
comment proving closure of a subset
And as seen there, simply writing down what one has to show almost completes the proof.
1d
comment Calculate remaining space of a box/cube
Reminds of the en.wikipedia.org/wiki/Knapsack_problem
1d
comment Which voting method is the most fair?
Most important point: Define fair
1d
comment Is complexity change when multiply with some number
Combining two $O(\log n)$ operations is again $O(\log n)$.
2d
comment What is the $\lor$ symbol?
... which suggests that the bar means negation and juxtaposition is lgical and (not multiplication). In other words $a\lor b = \overline{\bar a\bar b}$.
Jul
18
comment $x<y$ then $x^3<y^3$
Alternatively, $x^2+xy+y^2 = \frac12(x^2+y^2+(x+y)^2)\ge0$ with equality iff $x=y=0$.
Jul
17
comment Show that $\mathbb{Z}_p\setminus\{\overline{0}\}$ is not a group if $p$ is not prime.
To elaborate on @Mathmo123's comment: You merely show "There exist nonprime $p$ such that $\mathbb Z_p$ is not a group" while the problem statement is about "For all nonprime $p$, $\mathbb Z_p$ is not a group".
Jul
16
comment Explaining Infinite Sets and The Fault in Our Stars
@Kaz Yes I can, I just cannot place these in a bag in physical space with each ball having positive volume. But one gets similar problems already with countably many balls. I used this anecdote to literally tear apart the real numbers, depriving them of any disturbing properties (such as their topology).
Jul
16
comment What is an ordered pair actually?
@Brian More specifically, $(a,b)=(c,d)$ iff $a=c\land b=d$.
Jul
16
comment How many squares can be formed from n equidistant points in a circle?
@Crostul I reckon the points should be vertices of a regular $n$-gon