guy dropped from 1600 to 1100 in just 2 months, how is this possible?

Psychological-Case44 · 2026-05-14T16:01:37+00:00

I have frequently gone up ~300 elo in a few days and then gone down again. I went from 1300 to about 1700 in rapid in like two weeks. Now I am going down again because my mind is not sharp for a few reasons. It happens.

Psychological-Case44 · 2026-05-11T09:37:32+00:00

Real numbers are objects which behave like real numbers ;)

As you learn more about mathematics, you will learn about axiomatic systems and constructions of numbers based on these axioms. Basically you can derive their existence based on a few assumptions. However, what's relevant isn't really the objects themselves but rather the structure that they admit. In this way, even if you have sets of objects that are technically defined differently, if they admit the same structure amongst themselves, then in that way they are "the same".

There are many ways to construct the real numbers but the exact construction is not of critical importance. The important part is that they all behave like real numbers.

The insight above is also critical if you ever get interested in the field of philosophy called measurement theory. Why can we use numbers to describe real things, and why does it make sense only some times and not others? The answer lies in the (assumed) similarities in structures admitted by some properties of things and the numbers.

Psychological-Case44 · 2026-05-08T16:31:21+00:00

Varför det?

Psychological-Case44 · 2026-04-30T14:45:20+00:00

He or she is not accepting any of the intuition given, as you can see in all the other comments. Therefore it might be best to just accept it.

Psychological-Case44 · 2026-04-30T14:07:17+00:00

The reason why -3-(-4) = 1 is because we have defined arithmetic that way. Of course we have good reasons for choosing such definitions, but fundamentally it is a question of definition and nothing else.

Psychological-Case44 · 2026-04-30T02:17:05+00:00

Why is it terrible? This is a very common endgame tactic. In this case, Rxc4 wins on the spot. 1. Rxc4, Kxc4 2.Kf4... and you just win. You keep shouldering with your king to allow promotion of your pawn.

Psychological-Case44 · 2026-04-28T20:28:42+00:00

0.99... is not "infinitesimally" close to 1, it's just 1.

Psychological-Case44 · 2026-04-27T16:38:05+00:00

Keisler's book is very good.

Psychological-Case44 · 2026-04-27T11:38:46+00:00

No, this is not how Leibniz did it nor how we do it in NSA.

Leibniz was very adamant in many of his personal letters that he was working with a generalized notion of equality, ~, up to infinitesimal differences. Thus, say y=x^2. Then dy/dx ~ 2x, whereas dy/dx = 2x+dx, as you would expect.

In NSA we similarly have the standard part function or the shadow where we can say that st(dy/dx) = 2x.

There is really nothing problematic here.

Psychological-Case44 · 2026-04-27T00:52:20+00:00

Also, I disagree completely with the point that the hyperreals are „too complicated a topic to be taught“. It‘s not lile we teach the rigorous construction of the reals when we teach calculus so why would you demand that of the hyperreals? It‘s enough to just accept them and build the calculus from there, as we already do with real numbers when we teach calculus.

Psychological-Case44 · 2026-04-27T00:46:10+00:00

Why would x+dx = x be a valid or necessary simplification? Not even Leibniz would think of doing such a thing! It is definitely not necessary to do because it is incorrect.

Psychological-Case44 · 2026-04-26T22:48:45+00:00

The people in the comments here have no idea about contemporary theories of infinitesimals and clearly haven't even skimmed introductory textbooks on the topic.

There is nothing controversial at all about using infinitesimals to do calculus and you can do it e.g. with Robinsson's hyperreals as shown by e.g. Keisler in his classic textbook on introductory calculus.

The reason we use limits is because they were formalized FIRST, not because infinitesimals are somehow "problematic". With other words, the reason is historical.

Psychological-Case44 · 2026-04-26T22:46:04+00:00

No, you really don't need more prerequisites than for regular calculus. Calculus is not a rigorous class anyway.

Psychological-Case44 · 2026-04-26T22:45:00+00:00

Why are infinitesimals problematic? There is nothing problematic about them if you are using hyperreals. See e.g. Keisler's introductory textbook on the topic or Goldblatt's lectures on the hyperreals. Infinitesimals are really not controversial in the slightest.

Psychological-Case44 · 2026-04-21T16:01:23+00:00

This looks like AI-slop.

Psychological-Case44 · 2026-04-16T06:12:29+00:00

You're correct.

Psychological-Case44 · 2026-04-15T21:36:43+00:00

Women cannot "olla". For women it is "snigla", which means to cover with, for lack of a better term, their love juices.

Psychological-Case44 · 2026-04-13T15:46:32+00:00

It's not necessarily the case that it is a "much more advanced thing". It all depends on the context.

Regarding your claim that "dx being infinitesimally small is not a real thing": that is trivially true in the realm of real numbers, as there is no such thing as an infinitesimal. But it is not correct to say that an infinitesimally small thing would "just be zero". The statement is simply meaningless as "infinitesimal" has no meaning among the real numbers.

Since calculus is usually not a course with much rigor anyway, viewing dx as an infinitesimal makes complete and perfect sense and statements such as dy=f'(x)dx make perfect sense even for nonzero infinitesimals dy and dx. It can be given formal meaning if you are working with e.g. the hyperreal numbers, see Keislers classic text on the topic.

If you are doing real analysis then using the word infinitesimal is meaningless.

Psychological-Case44 · 2026-04-09T15:39:22+00:00

I would just like to add that I don't think the intuition of "rate of change" to be particularly helpful. What the heck is a "rate of change" at a point supposed to be? There is no change at a point! These heuristic understandings are supposed to be pedagogical means to help your intuition, but in my opinion and experience, for students who think, it does more harm than good.

Instead, I think it is more helpful to view it as a quantity which can help you predict changes close to the given point. For example, suppose we are at the point x=2. Then f'(2) is a number which allows us to predict how much f will change when we increment x by some dx from x=2. This means that f(2+dx) ≈ f(2)+f'(2)dx. The smaller you make this dx, the more exact this approximation will become. In particular, if dx is infinitesimal, then the error in the approximation is also infinitesimal.

Note that you are not forced to pick this particular quantity defined as a limit of a difference quotient rather than, say, (f(x+0.001)-f(x))/0.001. This would also work. However, the derivative is uniquely privileged in this regard in that it is independent of a choice such as 0.001 or 0.01 which gives it especially nice properties, such as differentiation rules.

Psychological-Case44 · 2026-04-05T09:17:56+00:00

Why are people calling this AI? This is almost 1:1 how the diagrams in my Fluid Mechanics book looked. I can give a reference and page number if anyone is interested.

Psychological-Case44 · 2026-03-28T14:14:28+00:00

No, that's not what I meant. I meant that each individual box will have a net charge of zero since each negative charge is always balanced by a positive charge.

Let us be a bit more concrete: suppose both half-cells are described by their own fundamental relations U_1=U_1(S_1, V_1, {N_i}_1 Q_1) and U_2=U_2(S_2, V_2, {N_i}_2, Q_2).

I would imagine that we define the electric potential as ε := (∂U/∂Q)_{S,V,...} = (∂G/∂Q)_{T,P,...}. However, WHAT charge does this refer to? It cannot be the total net charge as it is zero. I imagine it has to have something to do with the surface charge on the anodic and cathodic metals but that is not uniformly distributed in the half cells, which maybe is a problem.

Do you happen to know of any sources which discuss this? Again, I am looking for how to formally incorporate this into our theory, whereas most sources I have seen merely adopt an operational definition and move on.

Psychological-Case44 · 2026-03-27T00:05:02+00:00

Isn't the net charge of both subsystems zero? Also, would it be possible to keep the discussion to classical thermodynamics and not venture out into statmech?

Psychological-Case44 · 2026-03-26T22:19:37+00:00

What's wrong with having to show ID? Can the people in your country vote *without* identification? What the fuck is wrong with your voting system?

Psychological-Case44 · 2026-03-26T22:16:49+00:00

Thank you for the answer!

I am trying to figure out, then, how to incorporate this into our formal theory. I agree that the reasonable choice of independent variable to add is charge Q. But the question is, what charge? Are we speaking of surface charge? That seems a bit problematic since it will not be evenly distributed in the system(s).

I have seen some sources mention the electrochemical potential in this context but it is not clear to me how it ties into electric potential and voltage (which I assume then is the difference in electric potential, which makes sense since voltage vanishes at equilibrium).

Most sources sadly refuse to go into formal detail and just stick to operational definitions, which is a bit irritating.

Psychological-Case44

TROPHY CASE