jojomodding

Math is not about the definitions. It is about the connections between these definitions. And the techniques used to establish broader classes of connections between similar objects.

The way we formalize a connection is with a proof. And if the proof is "nice and modular" it sorta explains by itself how it can be used for similar problems.

And such proofs definitely belong into MathLib. There is often value in actually reading the Lean proof script (especially with the IDE support like jump to definition). It is not only there for the machine.

"Reading" a textbook is very different from reading a novel, that should be noted. You gotta do the exercises.

And who is "they" in this case?

Or alternatively, instead of evicting it all, can you move the data around in physical memory while updating the page table, so that you can clear a large enough continuous block of physical memory?

Not so fun fact: Mythicism around Proto-Indo-European is part of what made Hitler come up with the idea of "Aryans" because they hypothesized that there was some relation between the language having come from Iran (as "Urheimat") and then this leads to everyone wanting to be (indo)-aryan-decendent the most.

Yes it is true in the unique model of second order PA, aka the computable model, aka the "standard" model.

They still have scientific instruments operating. These have produced new insight into the last few years, telling us e.g. how large the Heliosphere is. The investment needed to find this out with a new drone would be astronomical (heh) whereas using the existing tools is basically free.

No, Lean allows non-constructive proofs so a proof could be like "if the Riemann hypothesis is true the counterexample is 42 otherwise it is the first nontrivial zero" or something like this, and then you don't get a fully closed counterexample.

Football was doing fine before this all started. It just multiplied the wages of some people who already earn more per year than I will ever own in a lifetime.

Yes. One way to do so is by eradicating gambling (or at least the ads for it).

People will never be 100% happy, all the time. And gambling (like many other companies) prey on people in the moments where they feel down.

Chaitin's constant. Or rather, you can never see that it has been laid out in your infinite universe.

They just need to have smaller fees than Visa/Mastercard.

Paying by SEPA direct debit in a store checkout situation seems insane. Even with instant payments it can take 20 seconds which is too long. Add to that the fact that users need to log into their online banking and the unfair leveling of risk onto the consumer.

This video is so insane. They're in a combustion engine. I can not fathom why they survived let alone managed to drive out of this. Trains are not build for fire resistance.

Is it gonna be one of those things where increased safety encourages dumb people because "it is watertight you know" so now a lot more people drive into the floods, and even though it's a smaller proportion more people in total drown.