Two sets with infinitely many things are the same size when you can describe a one to one mapping from one set to the other.

For example, the counting numbers are the same size as the counting numbers except for 7. To go from the former set to the latter set, we can map 1-6 to themselves, and then for every counting number 7 or larger, add one. To reverse, just do the opposite.

Likewise, we can map the counting numbers to only the even counting numbers by doubling the value or each one as our mapping. There is a first even number, and a 73rd even number, and a 123,456,789,012th even number.

By contrast, imagine I claim to have a map from the counting numbers to all the real numbers between 0 and 1 (including 0 but not 1). You can find a number that isn’t in my mapping. Line all the numbers in my mapping up in the order they map from the counting numbers, so there’s a first real number, a second, a third, and so on. To find a number that doesn’t appear in my mapping anywhere, take the first digit to the right of the decimal from the first number, the second digit from the second number, the third digit from the third number, and so on. Once you have assembled this new (infinitely long) number, change every single digit to something different. You could add 1 to each digit, or change them at random, or anything else.

This new number can’t be the first number in my mapping because the first digit won’t match anymore. Nor can it be the second number, because the second digit doesn’t match the second number. It can’t be the third or the fourth, or any of them, because it is always different somewhere. You may also notice that this isn’t just one number you’ve constructed that isn’t anywhere in the mapping - in fact it’s a whole infinite family of numbers that are still missing, no matter what order I put any of the numbers in, and no matter how clever my mapping seems.

The set of real numbers between 0 and 1 truly is bigger than the set of counting numbers, and it isn’t close, despite both being infinitely large.

I got 17/28… I do not use javascript. This is not the first time I have taken this quiz (but it has been a while).

It’s not just about slavery. There was also state’s rights (to slavery), and the economic disparity (turns out free men work harder than slaves?!), and a clash of religious ideals (people that interpret the Bible as pro-slavery vs people that believe benevolence requires abolition). There were even one or two spots where water usage rights and federal funding were in controversy.

I only buy generic brand medications, so my kids are at risk of generic brand autism. Is this going to be a signifier of a low income upbringing when they reach adulthood?

Should I switch to name brand Tylenol for their future?

It’s already been made perfect once. What updates would you make it divinely inspired code?

As with most news stories, you are still welcome to guess the Simpsons episode that predicted these events.

I distro hopped about every 4 months from ~12-22, never really feeling like I’d found the right platform. Sometimes I would dual boot (or just run) Windows, and for a while I had Windows XP in a state I could tolerate.

For several years after 22, I ran Windows at home, and kept Linux for work. I basically just wanted to game, and Windows was good enough for that. Finally, something came up that I needed a home server for, and I chose Arch, based largely on my experiences from several years ago. Arch had been more stable for me, and when it did break, it always felt like the tools to fix it existed. Ubuntu and derivatives broke for me mostly in “Oops, system is dead. Maybe reinstall?” ways, which I didn’t want on my server. Other distros gave me an assortment of problems, from updates taking too long, to lacking support for a WM I enjoyed, to driver issues.

Once I was regularly SSHing from Windows to Arch, I missed the things I could do on Linux (more than just games), and steam had made Linux support from a lot of games better, so I reinstalled my gaming PC as Arch too.

I added a lot of things to my server, and had more problems with some third party tools every time e.g. elasticsearch, mongodb, or postgres updated, so I added a kubernetes cluster with an immutable OS. I tried 3 before settling on Talos, and now when a workload on the server breaks, I move it to kubernetes. That pace has worked out for me, but now the server does no heavy lifting, so I’m experimenting with local LLM on it.

I suspect this is the (non-word) singular form of the noun “electronics”. If there’s a better term for such words, and you let me know what it is, I will give you my thank.

If small numbers are much more frequent, it’s better to return early. Really, you should gather statistics about the numbers the function is called with, and put the most frequent ones at the top.

You’re right, I want thinking of the manager thermals as counting as another person for the purposes of “alone with”, but provided they can move back and forth simultaneously with their employee (or they’re always counted as part of the new team) then the puzzle is possible.

It’s not, the way it’s written, the asshole cannot coexist with either the bore or the idiot, which is pretty accurate.

Ideas can only be patented, not copyrighted. If a company designs something novel enough to qualify for a patent, and so good that people willingly pay for the feature, that’s impressive, and arguably still a good thing. If instead they design a better user experience, or an improvement in performance, the ideas can be used in open source, even when the code cannot be.

They only came out 10 years ago. If we optimize now, how will we integrate an AI chat agent feature next year?

Delete Ass Master volume 7 to make room - that one wasn’t any good anyways.

They’re vaccers because they suck.

Which industry do you work in?

I love the idea (and it’s definitely true) that there are irrational numbers which, when written in a suitable base, contain the sequence of characters, “This number is provably normal” and are simultaneously not normal.

Wrong: I had a 1% chance, and I doubled my chances. Now my chances are 101%.

Right: I had a 1% chance, and I doubled my chances. Now my chances are 2%.

Wrighongt: I had a 1% chance, and I doubled my chances. Now my chances are 3%, because I’m a lucky person.

The belt and belt loops go all along the top row. If there’s only one row, the matrix can only wear a short-shorts version. There’s a crotch in each space between columns, and a leg on every column of length greater than 1.

Sparse matrices have their own special pants that are more efficient, of course.

With 17, I understand that you’re referring to how 299,999 is also divisible by 17. What is the 51 reference, though? I know there’s 3,999,999,999,999 but that starts with a 3. Not the same at all.