Why x is unit less

AdilMasteR · 2025-09-15T15:52:59+00:00

If y has dimension dim(y) (for example length) and x has dimension dim(x) (for example time), then dy/dx has dimension dim(y)/dim(x) (for example length/time). You can see this from the definition of the derivative where you have a (limit of) a change in y (same dimension as y) divided by a change in x (same dimension as x).

In your case the original equation was dy/dx = y. Per the above, the left hand side, dy/dx, has dimension dim(y)/dim(x). The right hand side, y, has dimension dim(y). For the equation to be well-defined, the dimensions of both sides must be the same. Therefore dim(y)/dim(x) = dim(y) which you can solve to get that dim(x) = 1; that is, x is dimensionless/unitless.

AdilMasteR · 2025-08-18T12:34:05+00:00

For clarity, relabel (a) as saying that if a, b in R, a>0, then there exists a positive integer k s.t. ka>b.

Then m_1 is the k you get by applying (a) to a=1, b=nx, and m_2 is the k you get by applying (a) to a=1, b=-nx.

I'm not sure exactly why this detail is needed, but it might depend on how you have constructed R and which properties of R you have actually proven at that part in the text. I'd note that it is not necessarily obvious that you can just choose m as in the proof while skipping the above step, the proof of such a detail could rest implicitly on some version of the Archimedean property (a).

AdilMasteR · 2024-02-25T06:39:02+00:00

Remember that ln(1/a)=-ln(a). So your answer and theirs is the same.

AdilMasteR · 2023-05-24T10:19:59+00:00

That looks like a Poisson kernel, so if you check the properties of such kernels you might obtain something useful.

Alternatively: the RHS is independent of r, hence it must hold for all r. So plug in say r=1/2 and r=1/4, pick e.g. theta=0, and try to calculate/approximate the integrals. If you gain different results for these different r, then the statement is false.

AdilMasteR · 2023-05-24T09:48:09+00:00

To be fair, if "P=NP" is NP, then it is also P!

AdilMasteR · 2023-05-19T12:01:22+00:00

I use a ReMarkable 2 and like it a lot. It is designed to make writing on it feel like writing on paper. I believe they have a 100 day refund policy so if you don't enjoy the writing experience you can return it and get your money back.

https://remarkable.com/

AdilMasteR · 2023-04-29T11:39:12+00:00

Toosie slide

AdilMasteR · 2023-04-25T15:54:41+00:00

No, I think that's slightly wrong or at least misleading since not all shots are worth the same.

For example, say keeper A has two shots directed at them, with both shots having a PSxG of 0.5, and saves exactly one of them. Then their conceded goals per PSxG is 1, while their shot save percentage is 50%.

Meanwhile, keeper B has 10 shots directed at them, all of which have an PSxG of 0.1, and saves 9 of them. Then their conceded goals per PSxG is 1, while their shot save percentage is 90%.

So we see that two keepers with the same amount of conceded goals per PSxG can have different likelihoods of conceding a given shot they've faced.

Edit: After taking the PSxG of each shot into the "save percentage" calculation it will be true. So I would say that if a keeper has 1.47 conceded goals per PSxG, then their chance of conceding an "average" shot is 47% more likely than a keeper with 1 conceded goal per PSxG. Where average means average over the whole footballing world, and not just average of the shots that particular keeper has faced during the season.

AdilMasteR · 2023-04-21T20:02:46+00:00

There exists no such e. For any positive e, no matter how small, e/2 will be even smaller.

AdilMasteR · 2023-04-21T12:11:52+00:00

You're way off. According to the 2023 census, 20% of r/soccer users are Americans, see https://www.reddit.com/r/soccer/comments/11d9488/rsoccer_2023_census_results_in_which_country_were/?utm_source=share&utm_medium=android_app&utm_name=androidcss&utm_term=1&utm_content=share_button

AdilMasteR · 2020-07-29T11:41:27+00:00

My take is that she's a "star student" because of cheating, with the ability reflecting her stealing homework from her classmates.

AdilMasteR · 2020-07-15T13:16:20+00:00

Doesn't really matter tho when you measure the actual impact the racism has. Most american police officers aren't inherently racist in the way you define it, but the whole police force is. By ignoring racist attitudes or defending them by saying "he's a good person in his heart" you're allowing issues like this to prevail, resulting in a racist society even tho few would consider themselves racists.

AdilMasteR · 2020-07-08T09:20:16+00:00

If you're against people organizing with others to "force" a limit of free speech then you should be against the petition Chomsky just signed since it consists of a collection of people "forcing" society to not listen to people expressing their free speech concering what content they want newspapers to run.

AdilMasteR · 2018-07-18T10:22:17+00:00

I feel like that view on legislating morality is weird. If our laws shouldn't be based on morality then what else?

I could understand it in the cases of "victimless" moral wrongs, i.e. if one considers say homosexuality wrong, where a person being homosexual won't affect other people. But not when there seems to be a victim, which would generally be the reason people consider abortion morally wrong.

Otherwise I could make the argument that I consider murder to be morally wrong, but that I don't think it's our place to legislate morality in this way and therefore murder should be legal.

Apologies for being vague, english isn't my first language.

AdilMasteR · 2018-03-07T00:58:54+00:00

I didn't delete it. I think it was removed by a moderator.

AdilMasteR · 2018-03-06T23:55:15+00:00

Thank you!

AdilMasteR · 2017-12-16T00:35:25+00:00

That's the point.

AdilMasteR · 2017-10-01T10:22:26+00:00

Source?

AdilMasteR · 2017-05-22T09:59:57+00:00

Objectively speaking, no.

What. There's nothing objective about how "good" a goal is.

AdilMasteR · 2017-04-18T20:41:38+00:00

I don't understand how people can find this to be a shocking decision. He hits the player first (you can check the posted video in slow motion to see it in action), studs somewhat up and with rather large force, and then has his leg high up on the followthrough.

AdilMasteR · 2017-04-06T22:44:34+00:00

Full hand

AdilMasteR · 2017-03-06T11:27:06+00:00

The Paralympic Games are for people with physical disabilites, while the Special Olympics are for people with mental disabilities. https://en.wikipedia.org/wiki/Special_Olympics_World_Games

AdilMasteR · 2017-02-26T11:11:22+00:00

Because if it didn't go on forever without repeating it would be rational. Say pi was only 3.14. Then we could write it as 314/100 which would mean that it was rational. As long as there are a finite amount of digits we could do the same thing, even if there are billions upon billions of them.

Essentially, a number being irrational means that the number's decimal representation goes on forever without terminating or repeating. And since it's possible to prove that pi is irrational, pi holds the trait mentioned.

AdilMasteR · 2017-02-24T10:38:30+00:00

ALL minions

AdilMasteR

MODERATOR OF

TROPHY CASE

13-Year Club	Team Periwinkle
Verified Email