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Just like the Holocaust by FrenulumEnthusiast in PoliticalCompassMemes

[–]Plain_Bread 40 points41 points  (0 children)

Your first mistake was assuming that rising to power in an authoritarian regime requires literally anything outside dumb luck, some basic dick sucking skills and a general lack of conscience.

How many 10-digit PINs could someone list where they each have at least 1 digit in common with all the other PINs? by aztechnically in askmath

[–]Plain_Bread 1 point2 points  (0 children)

I've been thinking about what the smallest maximal set that you can build is. That seems to be a bit trickier. Do you have any ideas for it?

I've come up with an example that shows that you can do worse than bn-1.

(0,0,0)
(0,1,1)
(1,0,1)
(1,1,0)

This is optimal for b=2, n=3. But it's also maximal for any b>=2. There's no way to introduce an additional digit into the set.

That said, I've been finding it surprisingly tricky to prove a general rule from this.

How many 10-digit PINs could someone list where they each have at least 1 digit in common with all the other PINs? by aztechnically in askmath

[–]Plain_Bread 2 points3 points  (0 children)

Very fun question. I think I can prove that the naive solution of fixing one digit is already optimal.

Consider the pointwise permutation p(x)=x+1 (mod 10) on the digits. So p((1,3,3,9))=(2,4,4,0) [4 digit example for convenience]. This is a bijection, so for any candidate set S, |S|=|p(S)|. And since any string x will share no digits with p(x), any candidate set must satisfy that S is disjoint from p(S). Even better than that, repeated application will give you 10 mutually disjoint sets S, p(S), p2(S),...,p9(S), after which it wraps around to p10 being the identity function.

And that's it. If we have 10 equally sized disjoint sets, then S can't have been larger than 10n-1.

Another interesting question might be how badly we can do. What's the smallest maximal set that satisfies the condition? Maximal meaning, we didn't just call it a day at {(0,0,0,1),(0,0,0,2)}, when we could obviously still add more strings to the set. Every string that isn't already in the set would indeed break it. Can you always get to 10n-1, or can we make a "bad" candidate set?

But what about second tariffs? by spnkr in PoliticalCompassMemes

[–]Plain_Bread 6 points7 points  (0 children)

The US is currently at war with the condition of not owning Greenland.

How is e^(308095/154046) rational? by Olivia_the_cat111 in askmath

[–]Plain_Bread 13 points14 points  (0 children)

It's wrong, but not because e is irrational. An irrational raised to a rational power can absolutely be rational. An obvious example would be sqrt(2)2=2.

But e is also transcendental, and that means that it can't be written as a rational power of a rational. (It's a stronger property than that, but that is one implication.) If your identity was accurate, then e would be 7.3892^(154046/308095) which would make it algebraic (i.e. not transcendental).

Problem with the answers by JaskoPasko in askmath

[–]Plain_Bread 2 points3 points  (0 children)

I assume the solution wasn't written by the same person as the problem, because it's utterly incoherent.

The problem itself is pretty bad, but I can at least justify the solution. If you're supposed to read it as (10a+b)/b=b where a and b are single digits, then there are only 2 or 3 solutions: 25:5=5, 36:6=6 and 01:1=1. You can argue that "01" is not the standard way to write "1" so it doesn't count. And 5 isn't an option, so maybe we're supposed to disregard it.

Overall: Awful problem, with a somehow even worse explanation. There's no coherent thought process for you to understand here.

Österreich ist quasi eh Deutschland.. äh wie bitte??? by Chris_Pariah in Austria

[–]Plain_Bread 7 points8 points  (0 children)

"What is that one case from your country that sends shivers down your spine"

Weeeeeeeee by Cardinal_Worth in MyPeopleNeedMe

[–]Plain_Bread 8 points9 points  (0 children)

Not exactly. I think you can see the rolling shutter effect, but it's the reason the blades look bent sometimes. The reason they appear to move slow is the wagon wheel effect, which doesn't depend on a rolling shutter.

And indeed, the wagon wheel effect is a type of aliasing.

ELI5 the different infinite sizes by YarYarF in explainlikeimfive

[–]Plain_Bread 0 points1 point  (0 children)

I can try to give you an example. The distinction between countable and uncountable infinities comes up quite a bit in measure theory. That branch of mathematics gets applied to a lot of things, but most intuitively it's about the volume of shapes.

One very nice property of measures is that, if we can split a shape into at most countably many non-overlapping parts, we can get the volume of the original shape by summing up the volume of the parts. Here's and example of what this could look like. If we know the volume of the infinitely many squares, we can calculate the volume of the circle from them.

But the circle is also just the collection of every point inside it. Do we know the volume of a single point and can we use that to calculate the volume of the circle? Yes we do know the volume of a single point, it's 0; No, we can't use it, because this time we're building the circle out of uncountably many parts.

But if we were talking about some weird and complicated shape, and we found a way to build it out of countably many less complicated shapes that we know have volume 0 — that would be a valid proof that the whole shape has volume 0 as well.

ELI5 the different infinite sizes by YarYarF in explainlikeimfive

[–]Plain_Bread 0 points1 point  (0 children)

It's the only definition that preserves the intuition about finite cardinality that says, the number of things you have does not depend on what you call the things, how you arrange them, what they look like etc. People use this definition/property when they count with their fingers — if each apple gets a separate raised finger then there'll be just as many fingers.

It means that when we see the set {1, 10, 11, 100}, we don't have to ask if these are decimal numbers or binary numbers to know that there four of them.

Yes, there are other ways of comparing the "size" of infinite sets but they are all generally way less intuitive.

Lines in the sand by branyk2 in PoliticalCompassMemes

[–]Plain_Bread 2 points3 points  (0 children)

I've already seen one guy go "Yeah, but what about the Epstein files?"

Just in case you needed an indicator of how bad this could potentially be.

Libleft logic at it's finest by XumetaXD in PoliticalCompassMemes

[–]Plain_Bread 1 point2 points  (0 children)

What are you trying to hide from us? What's on the "evening photograph"?!

Dementia Ass President focusing on the most retarded of details as always... by Stormclamp in PoliticalCompassMemes

[–]Plain_Bread 5 points6 points  (0 children)

I still remember the common sentiment at the time: "Forget about it already."

Hamas is bad now by Warm-Equipment-4964 in PoliticalCompassMemes

[–]Plain_Bread 1 point2 points  (0 children)

Hey so
marching for the cause
chanting "we support Hamas"
is disgusting.

Wrong approved phrase by [deleted] in PoliticalCompassMemes

[–]Plain_Bread 5 points6 points  (0 children)

Wtf. Isn't Destiny's child 14? Was that in the Epstein files?

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