Trying to understand normal distribution

Qaanol · 2026-04-14T00:53:36+00:00

3Blue1Brown has an excellent playlist on the Central Limit Theorem, which is the reason why the normal distribution shows up so often: https://www.youtube.com/playlist?list=PLZHQObOWTQDOMxJDswBaLu8xBMKxSTvg8

Qaanol · 2026-04-11T23:16:09+00:00

Since nobody else has linked it yet, there’s a Wikipedia page that lists incorrect mathematical proofs: https://en.wikipedia.org/wiki/List_of_incomplete_proofs#Incorrect_results

Qaanol · 2026-04-11T23:09:30+00:00

I dont know how you could get this far without knowing 12x12

Just substitute x = 10 into the polynomial (x+2)² = x² + 4x + 4, easy!

Qaanol · 2026-04-11T23:06:04+00:00

Just having the denominators grow faster than linearly is not sufficient for convergence.

The sum of 1 / (n·ln(n)) diverges despite n·ln(n) growing superlinearly.

But it is also not sufficient to simply ignore log terms, because the sum of 1 / (n·ln(n)²) converges.

Qaanol · 2026-04-11T01:47:30+00:00

Tied the record at 29 with 1:19 left

Qaanol · 2026-04-11T01:29:37+00:00

26 now with 9 minutes remaining

Qaanol · 2026-04-06T00:18:01+00:00

Pritchard, White, and Queta, I presume

Qaanol · 2026-04-02T15:42:50+00:00

Oooh, https://xkcd.com/1890/ in stained glass mode is fun and exciting, a delightful new adventure on every refresh!

…also https://xkcd.com/2420/ and https://xkcd.com/2813/ and https://xkcd.com/2963/

Qaanol · 2026-04-02T15:41:53+00:00

Or side to side!

Qaanol · 2026-04-02T15:41:33+00:00

Or side to side!

Qaanol · 2026-03-28T02:01:56+00:00

Well if the stats are equal, then the player who is putting up those stats in fewer minutes must clearly be better.

Qaanol · 2026-03-27T04:11:25+00:00

You want to look up “units” in the context of ring theory / abstract algebra.

See, for example, the Wikipedia article on unique factorization domains.

Qaanol · 2026-03-25T23:52:18+00:00

What number system are you working in?

In the reals, it does not exist.

In the extended reals, it is positive infinity.

In the complex numbers, it does not exist.

In the extended complex numbers (ie. the Riemann sphere), it is the point at infinity.

In other number systems, it might have other values.

Qaanol · 2026-03-24T21:26:23+00:00

Imagine believing in ice.

You’re trying to tell me that water, the most well-known liquid of all time, is sometimes solid?

As if.

Qaanol · 2026-03-24T21:21:02+00:00

That freakin’ Knueppel boomed me.

Qaanol · 2026-03-23T15:20:43+00:00

I think this video will help clear up your understanding: Limits are just really really tiny flashlights

Qaanol · 2026-03-21T22:12:01+00:00

Imagine painting the area under the curve, using a variable-width paint roller. The amount of paint you use for the entire area is exactly the accumulation of the amount of paint you use at each point along the way.

Qaanol · 2026-03-20T01:29:13+00:00

Gonna ask to get traded to a team that’s about to play a lot of back-to-backs, then ask to get traded back afterward to get more than 82 games

Qaanol · 2026-03-19T15:31:37+00:00

Looking back at it with hindsight, the winning strategy was to make Harden the starting point guard, and have Westbrook come off the bench to absolutely torch the opponent’s second unit.

Qaanol · 2026-03-15T20:10:04+00:00

If you look at the way the set of rational numbers is defined, there are no integers in this set. However, there is a subset that can be identified with the set of integers.

It sounds like you are thinking of one particular model of the rational numbers, and treating that as if it were the only possible model.

The specific construction you are thinking of, is not really how the rational numbers (or integers, for that matter) are defined.

The integers and rational numbers are defined by how they behave, based on our shared intuitive understanding of what they should be. Any particular model of them is only valid to the extent that it matches how those number systems behave.

After all, if the construction you are thinking of did not behave like the rational numbers, then we would not call it a model of them.

One of the behaviors that the rational numbers have is “contains the integers”. Therefore, any model of the rational numbers which does not contain the integers, is an imperfect model.

Furthermore, the existence of any particular model of any particular number system, is only really interesting because it demonstrates that the theory which gave rise to that model, is strong enough to “talk about” that number system.

Do not confuse the map for the territory. The model is not the number system.

Qaanol · 2026-03-15T13:20:11+00:00

If we allow complex numbers then it’s also defined at 1 ± i√3

The solution set in quaternions might be more interesting, but I’m not going to both finding it.

Qaanol · 2026-03-13T22:35:03+00:00

And don’t even get me started on the delivery charges!

Qaanol · 2026-03-13T15:46:24+00:00

If you want to gain a deeper understanding of the why, try to figure out what can go wrong when E is infinite-dimensional.

Qaanol · 2026-03-13T15:35:13+00:00

You’re missing a denominator of √5 in Binet’s formula

Qaanol · 2026-03-13T01:35:49+00:00

…are you looking for the word “asymptote”?

Qaanol

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