@leslietownes huh?

Oh. Scalar multiplication

Not scalar product

@EE18 to show two numbers are equal, show their difference is $0$

@Obliv I think this is perfectly fine

@AlessandroCodenotti any progress on that question about $A\subseteq \mathbb{R}^3$ consisting of points $(x_1, x_2, x_3)$ with exactly one $x_i$ rational being connected?

I didn't think about it, but I have 10 minutes now

Let's see, what happens in $\Bbb R^2$?

Its totally disconnected there

thats because $(r_1\pm x, r_2\pm x)$ for $r_i$ rational and $x$ arbitrary lies in the complement

but for $\mathbb{R}^3$, the same trick doesn't work, it makes up some kind of net instead of a $2$-dimensional surface you could enclose points with

one thing for certain is that $A^c$ is connected

sure

that's all I came up with myself

Hmm yeah it's not clear

I have a really terrible question

say your warping functions in some warped product metric satisfy some differential equation. What conditions allow one to pass the differential equation onto the geometry described by the metric?

nevermind

@JohnZimmerman that's terrible

just joking I don't even know what this means

I realized

that this question needs revisions

yeah I'm not insulting your intelligence or anything

explaining that this is a joke is just in case someone thinks I'm being rude

@JohnZimmerman This looks like word salad to me.

yeah it definitely looks like a word salad, but maybe ODE and differential geometry people understand it

there's definitely a lot of definitions in differential geometry that I have no idea about

Lie algebras aren't one of them

@XanderHenderson Well you maybe correct. The warping function $g_t(x)$ depend. on some time parameter $t$ changes the geometry of the manifold by changing $t$ itself

so I don't have a good grasp about what occurs when $g_t(x)$ is also depend. on a partial differential equation

This still looks like word salad to me.

sufficiently nice one of course

What is a "warping function"?

What is "the geometry" of a space?

How does a function "depend on" a DE?

$$g_{\phi} = \frac{1}{\phi_t(u)^{2}}\, du^{2} + \phi_t(u)\, dv^{2}.$$

for example

What is a "warped product metric"?

What does it mean to "pass a DE onto the geometry described by a metric"?

Warped product is a generalization of the (semi-)Riemannian metric used on a product manifold

As @Jakobian said, it is very possible that an expert in whatever part of mathematics you are studying might know what you are talking about, but to me, it is nonsense.

Xander these are amazing questions!

But the “pass a DE onto the geometry” makes no sense to me

@JohnZimmerman No, they are not "amazing" questions. These are the basic questions that you should be able to answer before you even pose the question that you are trying to ask.

You need to know the answers to these questions, and you need to be able to explain those answers to others. Otherwise, you are jumping into the deep end, and you need to go back and revise.

why can't pose them retroactively assuming i can do so in <k days where k is a very low constant?

For example, one of the motivating questions of my phd work could probably be summarized by the sentence "Under what conditions does the geometric zeta function associated to a metric space which carries a measure provide meaningful information about the geometry of that space?"

To an outsider who is not immersed in the very niche field I work in, I expect that this is word salad.

because we're too lazy to find a meaningful way in which something makes sense unless its very basic stuff

If I were to ask someone else a question about that work, I would need to be able to explain what I mean by a "geometric zeta function", what aspects of the "geometry" of a space are "meaningful", and what kinds of conditions might be reasonable to expect for a metric space carrying a measure (e.g. in what ways are the metric and measure compatible or not?).

I thought we were talking about metrics in geometry and not about metric spaces

@Jakobian I was giving a completely different example.

oh, right

it was so similar to what @JohnZimmerman is trying to do in recent days that it blended in

@XanderHenderson I meant that your questions were good

@JohnZimmerman I know what you meant. But my questions are only good in the sense that they are the basic, most fundamental questions that you should be able to answer while posing the question that you are asking.

These are not insightful or deep questions.

It is the basic kind of thing you need to be able to do for yourself.

@Thorgott OK, I will think on this. I am not sure what you and the author have in mind in terms of using still, but maybe it will come to me while I bike to work today...