mathematic

A major problem between them is trying to describe what goes on inside a black hole.  GR ends up as a singularity. QM says impossible.

1. All evidence points to accelerated expansion.

2. Singularity is a mathematical artifact.  Physics is unknown.

3. Pre-big bang is pure speculation.

It looks like the min and max occur when sin = 0 (0 or 180).

Opposite version of black hole?  What does this mean?

Use inverse squarer relationship.  Your description doesn't describe the motion of the first two relative to the third.

It will depend on where the observer is relative to the meteorites.  Speed of sound is not subject to Lorentz transformation.

Zeno's paradox goes away when time is considered.

Why is the name of a particular specialty important?  I presume venomology is narrower than toxicology.   Try Google.

How about "unmasking"?

The link appears to be a list of numbers - no picture?

Draw a picture!

My statement is about all (including complex) numbers.

Every number (except 0)  has two square roots.  Using the convention (ignore negative root) leads to these kinds of problems.

l

square root  of n(n+2) is approx. n+1.

Non-empty open sts must have positive measure, so your approach to the first question is correct.  The second question is almost from the definition.

1 hour ago, fmaths said:

Hi, I've been working on some Lebesgue measure and Lebesgue integral exercises for a few days and I have some doubts.

I need to say if the statements are true (I need to prove it) or false (I need to give a counterexample).

    Let $f:E\subset\mathbb{R}^n\rightarrow\mathbb{R}^n$ such that $|f(x)-f(y)|\le|x-y|$ for $x,y\in\mathbb{R}^n$, then $f$ transforms null measure sets into null measure sets.
    If two integrable functions agree in a dense set, the value of the integrals is the same.
    If two functions agree in a dense set, one of then is measurable if and only if the other one is also measurable.


For the first one, \textbf{I have no idea. I only now it's true since Lipschitz function is like that}.

For the second one, I know it's false. I've thought of considering two functions $f,g:[0,1]\rightarrow\mathbb{R}$ defined as follow:

\begin{equation*}

f(x) =

\begin{cases}

1 & \text{if $x\in\mathbb{Q}$}\\

0 & \text{if $x\notin\mathbb{Q}$}

\end{cases}

\end{equation*}


\begin{equation*}

g(x) =

\begin{cases}

1 & \text{if $x\in\mathbb{Q}$}\\

\displaystyle{\frac{1}{q}} & \text{if $x\notin\mathbb{Q}$, $q\in\mathbb{N}$}

\end{cases}

\end{equation*}


These functions agree in $\mathbb{Q}\cap[0,1]$. \textbf{Here, I don't know how to prove that $\mathbb{Q}\cap[0,1]$ is dense on $[0,1]$}.


For the last one, I also know it's false. We could take a not measurable set $E$ et let $f=\chi_{E}\cdot\chi_{\mathbb{I}}$ et $f=g$, where $g$ s'annule sur $\mathbb{Q}$. \textbf{I don't know how to prove that $f$ is not measurable}.


I'll be duly grateful for any help.

 

The second and third easily false.  The two function could agree on the rationals, but not elsewhere.

You need to use another deliminator for Latex $ doesn't work here [math] and [math] with / work.

Looking at the original question (I have not plowed through the responses), the ball on chain can hit harder than the hammer because it can be made to go much faster before release.

Pure speculation.  High wind conditions could lead to evolution of very sturdy thick trunk trees which would mitigate winds and allow small (compared to tree size) animals to evolve.

Mathematically sqrt(1) has two solutions +1 and -1.  There is a convention that only +1 is allowed and the program may be set up to follow the convention.

9 hours ago, Bufofrog said:

Agreed, I was using a DC example so the electrons would move in the direction of the current.

The point I am making is the speed of the electrons is irrelevant to electricity working.

Most households use AC where the electrons jiggle in place.

I don't get it!

Is there a question?  What are N, x, y?

Quote

Regarding the essence of space as 'pointy' has infinitely many zero dimensional matrixes whose closed regions can and, at the same time, cannot be smaller than themselves

I hate to say this, but it sounds like meaningless wordplay.

Sorry!  Completely strange to me.