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Where I live, any rental building from this century will be marketed as luxury. There is in fact absolutely nothing luxury about them. Everything is cheap and crummy, just not too dirty/smelly/with rats (yet). Rents are 5-7k for a 2b and being luxury or having amenities have nothing to do with this. Supply and demand do. There are enough people who make this kind of money and value living in a place that is half-decent + easily commutable to the city more than the 6k.

If PaaS or some "run container as a service" setup can work for your use case, I'd probably go with that. It takes care of many things K8s does without all the baggage. Also you are not investing into anything that doesn't port easily to K8s in the future.

On the other hand, if you are thinking of using bare VMs, then better go with managed K8s. I think in 2025 it's a draw in terms of initial setup complexity, but managed K8s doesn't require constant babysitting in my experience, unlike VMs, and you are not sinking hours into a bespoke throwaway setup.

I had to replace a perfectly good T450s because of terrible performance when using external 4k monitors. I had it for 6 years, upgrading everything I could, and it could probably last for at least another 4 hears if not for the outdated CPU. Replaced with a ryzen elitebook because RAM is expandable to 64Gb, hoping it will last for up to 10 years. The difference in performance is staggering compared to the old core i5, well worth the cost of a base model.

Definitely not. Mine is 16 and it will start swapping after running KDE, jetbtains, firefox and a couple electron apps for a few hours. It is tolerable, but in a year or two it won't be. Good thing it supports up to 64.

Surprised to see Velleman's book so far down. It taught me that proofs are fun and do not in general require clever tricks. As a bonus, it provided plenty of practice with foundational objects such as sets, relations and functions. All this made me much better at doing mathematics and prepared to texts in real analysis, CS, algebra.

CRDTs are useful to be aware of, but they are not a silver bullet they might appear based on the paper and online sources.

They are conflict-free only because they hide conflicts by forcing a consistent order on concurrent updates. How do they do it? By using logical clocks to version events. A logical clock is not magic. It orders concurrent events arbitrarily. Is this correct? In practice, probably not, meaning that more recent updates can be lost in favor of less recent updates. What does 'recent' mean? For a user it means latest in physical time. Just because the system doesn't know any better than to arbitrarily order a pair of events (that appear concurrent), doesn't mean the user doesn't know which event comes first. This is why not everything is implemented as a CRDT and conflicts will always exist in use cases where updates must never be lost.

A CRDT is a way to solve multi-leader replication without having the application code resolve conflicts.

This is what is required to build an app where any instance (node) can be offline for an arbitrary amount of time, but still be able to share state with the rest of the nodes when it's reconnected.

To implement this, every application node keeps a vector clock per register (an atomic piece of shared state). The vector clock allows any node the compare its own version of the register with the state received from any other node. Two values of a vector clock can either be causally related (in which case the most recent write wins) or concurrent. However the concurrency is from the system's perspective, but not necessarily from the user's perspective. An extra physical timestamp can be kept at the register level to order concurrent updates in a way consistent with the user's time perception.

Now, having the hybrid clocks in place to version each register on each node, the system must implement a protocol to ship every register update to all nodes (reliable broadcast).

Once all updates are shipped to all nodes, it's guaranteed that all nodes have the same (most recent) state.

(I built an offline-first product and had to roll my own protocol)

Sounds like you might simply not understand the definitions for these operators and symbols. In other words, it's not a notation problem. I find that it's helpful to mentally replace the symbols like dy/dx, sum, lim, integral, and so on with the concepts they represent. That is, go from operators to definitions.

I worked through this book to learn how to do proofs. It turned out way more fun than I expected. The book really did demystify proofs for me. It took several months of studying - there are many exercises. But completely worth it. I'm glad I have read this book before studying Group theory and Real analysis.

I'm studying for a Math BSc with the OU and I think their books are great. They are designed for 100% self-study and are polished over the years. The range of topics in level 1 math courses such as MST124 or MST125 is huge, while keeping the appropriate level of difficulty.

They seem to be scanning your email inbox and detecting which companies you have an account with. They they send a data removal request to one of these companies "on your behalf". When a company receives this request, of course it's not going to just delete your data since a request is coming from a third party. So they will either disregard the email, or in the best case they will contact you directly for confirmation. It seems to me that you have to give up access to all of your email to some startup just to be able to do GDPR requests with extra steps for everyone.

Well, this is just a bunch of nonsense.

Here are the logical ways to explain the misconception of injury being less common with bodyweight training:

1. Progress with BW is slow as crawl. All things being equal, lifting will improve strength much faster, leading to higher loads sooner. Higher loads always mean more injury potential. Faster progress is not magic - it's possible because all major muscle groups can be loaded precisely and gradually with weights as opposed to BW movements. You can take things as slowly as you want.

2. With BW, some movements simply cannot be loaded properly. For example there is nothing you can possibly do with just your body weight to put any serious load on your legs or low back. This already cuts one's potential for injury in half at the cost of neglecting the development of the lower half of your body. So instead of taking things slow with your barbel squats, you are stuck at 1-leg BW squats forever, which are only hard because of balance/stretching issues and are fairly trivial strength-wise.

3. With free weights, it's easier to be stupid and bite more than you can handle.

As I said, I've done both for enough time to appreciate pros and cons. There are reasons to practice BW training, but lower injury changes is not a good one.

Where's the less chance of injury part coming from? It's much easier to master and incrementally load a fundamental weightlifting movement than a corresponding bodyweight progression. This means better form and more control - fewer injuries. I have tried both types of training for a while, and have concluded that weights are superior in every way. Unless the goal is mastery of a specific bodyweight skill.

I didn't like SS when I tried it. It users the rep range 3-5 for the working sets as far as I remember. This makes sense as the book is strength-focused. However this is just too heavy for a casual lifter. Lifting 5RM, the form and concentration has to be very tight not to screw up. I've gotten small injuries from lifting much lighter than that. Nowadays I wouldn't even consider lifting 3RM for reps without backup - I know that will not end well.

I recommend 5/3/1 for everyone, especially with some lifting experience. Very easily sustainable long term because training sessions are short and sweet. Minimal risk of injury because the warm-up sets are built-in and there's no fatigue from long workouts. It can be easily combined with other sports like running or martial arts because there's plenty of time for recovery.

A better idea is to not develop insulin resistance in the first place and improve sensitivity.I eat 85% carb diet. My blood glucose barely moves up after eating a bunch of straight sugar, then goes back to fasting level after an hour and a half.