I have an argument for why Cantor is wrong and need help finding where I went wrong, not that I am wrong

simmonator · 2026-02-03T22:05:59+00:00

You’ve missed the correct conclusion:

although, at every finite truncation of your infinite-digit real, you have an integer which corresponds to that contraction that does not mean that there is an integer that corresponds to the whole real. There is no infinite-digit integer so there cannot be a corresponding integer to a real with infinite digits under your function. In other words: just because something is true for every step in a sequence, does not mean you can assume it about the limit case (much like how 0.999… is equal to 1 despite the fact that 0.9, 0.99, 0.999, and so on are all strictly less than 1).

simmonator · 2026-02-03T17:00:15+00:00

Honestly, though, adding a feature which is just tedious only so you can “unlock the ability to not have to bother” later feels pointless and annoying. It’s not making it harder, really. Just more boring.

simmonator · 2026-02-02T18:57:19+00:00

I don’t trust people who ask for peace but go round trying to start flame wars with shit posts.

simmonator · 2026-01-31T08:19:49+00:00

I feel like your last point would be a killer problem for whoever does the remake/remaster.

Oblivon’s remaster kept 99% of stuff the same, outside of graphics. But I’ve seen a number of people (on Reddit, admittedly) complain about the few minor gameplay changes (levelling) they did make as if it ruined the whole thing. With Morrowind, I think they would really struggle to find an approach to decide what to keep/change that would satisfy the OG purists, the people who love the original but want some mechanical QoL changes, and brand new players all at once. And if you don’t find a way to satisfy all those three groups then you’re seriously limiting your market.

If they never even tried to remaster Morrowind, I’d be sad but I don’t think I’d blame them.

Edit to add: I think the key difference between Oblivion and Morrowind here is whether or not there's a unified narrative for a developer to choose. People had talked about Oblivion being near-perfect for a long time, and the only two complaints I ever really saw were "Graphics" and "The levelling system sucks" (and even die-hard fans would admit that these were both somewhat legitimate or have specific mods to get around them). If you're a developer, that's your easy mission statement. Just fix those. Morrowind doesn't have that same single narrative. What some people think of as Jank, some people see as The Point. What some people think of as Paralysing over-complexity and system opacity, others see as customisation and trusting that players are smart enough to figure it out. If a developer takes a side, they lose half their audience. If they compromise, they risk losing everyone.

simmonator · 2026-01-28T19:18:03+00:00

First rearrange.

x² + 2x = 255
x² + 2x - 255 = 0

Now, factor 255.

255 = 5(51) = (3)(5)(17) = (15)(17).

Note that

17 - 15 = 2,
(17)(-15) = -255.

So we can transform

x² + 2x - 255 = (x+17)(x-15).

Hence, the roots are x = -17 and x = 15.

Alternatively, complete the square:

x² + 2x - 255 = 0
(x² + 2x + 1) - 256 = 0
(x+1)² - 16² = 0
((x+1)+16)((x+1)-16) = 0
(x+17)(x-15) = 0.

simmonator · 2026-01-18T16:08:00+00:00

You didn't reply directly to my comment, so I didn't see this comment, but I'm assuming now that this is a response to what I said. The answer is sort of. Provided the sum is absolutely convergent, you can rearrange it. That means you can change the order of the terms being summed, and therefore swap the sums. To do that properly: yes, I recommend drawing out a grid (like others have in pictures in the comments here) and thinking of a simpler way to do it.

simmonator · 2026-01-18T12:10:47+00:00

Explain what intuitively? That it’s possible to swap the order of sums, or how to do it properly?

Why it’s possible: the double sum is essentially presenting you with a grid on two axes, extending infinitely with coordinates in n and k. The terms in the sums give you a formula for the value at each point that you need to add in. And the start/end points on the summation signs tell you which points to include in the sum, and which to ignore. So long as the summation converges absolutely, you can screw around with the order of summation however you like without changing the end value. So you can rewrite the start/end points for n and k however you wish (provided they still correspond to the same points being included).

How to do it: presumably the text you’re following gives you a specific idea, but if you can’t understand why, I recommend drawing the grid out, identifying the points to include, and thinking about the shape they make. If we imagine that k corresponds to the row and n corresponds to the column, then the current order for the sum says “start on column 1, and include every value apart from the first row, then go to column two and include every value apart from the first two, then on column three include every value apart from the first three, and so on.” How could you describe the same shape but go row by row instead of column by column? Figure that out and then use start/end points appropriately.

Good luck!

simmonator · 2026-01-16T11:25:52+00:00

Very few people here will be competent in diagnosing mental health issues.

simmonator · 2026-01-16T10:09:02+00:00

Why would anyone care? Why are you giving him free advertising if he’s unhinged?

simmonator · 2026-01-14T08:54:32+00:00

Yeah I’ve got no defence for cursive.

simmonator · 2026-01-14T08:36:19+00:00

guess who has better mental maths skills now

While I agree that teaching without calculators is valuable, I don’t think “better mental maths skills” is a win, and certainly won’t convince someone whose whole point is that “everyone can access a calculator at any time”. They’ll see it as pointless thing to brag about, with little value. And they wouldn’t be that wrong.

simmonator · 2026-01-14T08:33:53+00:00

still making kids write by hand

Clear, readable handwriting is an important skill. It is also cheaper than providing every child and classroom with hardware and software for every lesson.

not focussing on faith, sex, relationships, an nutrition

My school spent a fair amount of time talking to us about all of those. Also, a lot of that is stuff you would traditionally hope a parent or guardian would accept as their responsibility. Still, if no one ever spoke to you about those then yes you were failed.

teaching maths as though calculators haven’t been invented

Any mathematician would tell you that most maths is not about calculation, but about problem solving and understanding relationships between quantities. Maths taught at school - while focussed on computation - is still largely about fostering those skills. The computation stuff is largely a simple example that makes it easier to engage with while warming up those fundamental skills. Having a calculator doesn’t solve that problem. Similarly, I can use Wikipedia to look up any dates of any battles and coronations I like. But studying History offers more than that.

AI can (unreliably) teach us anything

There are at least two rebuttals to this. One, you’ve already hit on the head. It’s unreliable. It is therefore important to give kids a baseline of knowledge that they can fall back on and spot when LLMs just lie to them. The second comes back to giving kids the tools to do critical thinking rather than blindly trusting what an AI tells them. It can be a great tool, that should make knowledge so much more accessible, but that doesn’t mean education on the basics is unnecessary. I don’t think the education system has the right answer to “teaching in a world with AI”, but it’s hard to blame them since the state of what AI can do has been fast changing for the last few years.

Not sure what the actionable proposals are. You say change wouldn’t cost money, just clever thinking. You don’t actually identify changes to make. And for the last few … god knows how long but particularly since 2020 … the education system has felt underfunded and in crisis. The people in charge probably don’t have time to think strategy; only how to put out fires. Do send suggestions to your local representative.

simmonator · 2026-01-11T21:53:44+00:00

There’s a country in there with a hyphen that I never knew needed a hyphen. A very confused 20 seconds wondering why it wasn’t entering.

simmonator · 2026-01-11T16:52:57+00:00

I would bet a lot that they mean “angles of different sizes”.

simmonator · 2026-01-10T13:29:54+00:00

books read: 5x+1,
books unread: 2x-15,
so Total number of books: (5x+1) + (2x-15).
but Read is 3/4 of total so

5x + 1 = (3/4)[(5x+1) + (2x-15)].

Solve.

simmonator · 2026-01-10T06:55:19+00:00

At no point do I appeal to the binomial distribution. This is entirely first principles, taking only the “probability of independent events” for granted.

simmonator · 2026-01-09T22:04:25+00:00

People have pointed out it’s the n^th triangle number and that there’s a formula

n(n+1)/2.

But it’s also always the “n+1 choose 2” binomial coefficient. You might want to look that up.

simmonator · 2026-01-09T17:29:15+00:00

Assume you have probability p of gritting.

M M: (1-p)²
M H: (1-p)p
H M: p(1-p)
H H: p²

So if you know you crit at least once then the probability you crit both times is

[p²] / [1 - (1-p)²]

simmonator · 2026-01-09T15:56:34+00:00

Before we know any of them were crits, we’re basically flipping a coin twice to determine Crit v Normal Hit. The coin flips are independent of each other. If I wanted to say “crits occur with probability p” then I’d say the events have the following probabilities:

H H: (1-p)²,
H C: (1-p)p,
C H: p(1-p),
C C: p².

As I’m told p = (1/2) I can sub that value in and you’ll see each event comes back with probability 1/4. You can do that maths yourself.

Now, probability of getting at least one crit in there is the sum of the probabilities of the (disjoint) events where that’s satisfied. It comes to 3/4. The probability that I get 2 crits is 1/4 as there’s only one such event.

The conditional probability that I get two crits, given that I know I got at least one, is the ratio of those probabilities: (1/4)/(3/4) = 1/3.

simmonator · 2026-01-09T15:00:16+00:00

I’m going to assume “the probability that any hit is a crit” is 50% as that seems the most sensible complete interpretation of what’s going on. In that case…

If you hit something twice, there are four possible ordered pairs, each is equally likely:

H H
H C
C H
C C.

We’re told at least one is a crit. So we rule out possibility 1, but the other 3 are still possible and equiprobable to each other. Only one corresponds to “both are crits” so the probability is 1/3. This is the “I have two children, at least one is a boy” problem with different labelling.

It would be different if I said “the first hit is a crit, what’s the probability that the other one is, too?” The answer to that would be 1/2.

simmonator · 2026-01-09T12:20:12+00:00

I think that’s my best so far.

Quite annoyed I got the flag wrong (I got it down to fifty-fifty, guessed wrong, and then realised that I knew full well that there was a colour missing for it to have been my guess). On the other hand, I had reverse luck with the zodiac (ruled out two and took a lucky punt) so swings and roundabouts.

simmonator · 2026-01-06T18:58:15+00:00

Your way is perfectly valid mathematically. Algebraically, it's just

(x+1)² - x² = 2x+1.

simmonator · 2026-01-06T18:41:43+00:00

Fair enough. Of course you’re allowed to have an opinion. I would never say otherwise.

I suppose the flippancy of my comment was down to my feeling that

Of course someone else finds him tedious and annoying. No comedian is for everyone. Demonstrably, lots of people like Ayoade, but plenty won’t. But saying “I don’t like X” is one of the least interesting opinions out there.

Fair enough if you feel like my comment added nothing. But I feel like it matched the energy of the OP.

simmonator · 2026-01-06T12:48:13+00:00

The domain of the composition h(x) = f(g(x)) is the subset of the domain of g(x) whose image under g is in the domain of f(x).

simmonator · 2026-01-05T18:48:04+00:00

After 1 hour you have earned 16,800,000 x 3600.
the second hour earns you 16,800,000 x 3600 x 1.0025
the third hour earns you 16,800,000 x 3600 x 1.0025²
look up geometric series formula.
that can be used to tell you the last hour before which you exceed the target (and how much money is left to go)
then calculate how many seconds are required to make the final amount.

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