It’s a definition from a well-respected global standards organization. Can you name a source that would provide a more authoritative definition than the ISO?

There’s no universally correct definition for what the ≈ symbol means, and if you write a paper or a proof or whatever, you’re welcome to define it to mean whatever you want in that context, but citing a professional standards organization seems like a pretty reliable way to find a commonly-accepted and understood definition.

Sure! See ISO-80000-2

Here’s a link: https://cdn.standards.iteh.ai/samples/64973/329519100abd447ea0d49747258d1094/ISO-80000-2-2019.pdf

“Approximately equal” is just a superset of “equal” that also includes values “acceptably close” (using whatever definition you set for acceptable).

Unless you say something like:

a ≈ b ∧ a ≠ b

which implies a is close to b but not exactly equal to b, it’s safe to presume that a ≈ b includes the possibility that a = b.

I was tilling my garden a month or two ago and got to one end, turned around, and casually strolling right through the middle of the plot, literally 10 feet in front of me and a very loud tiller, was a young buck. Completely unafraid of me or the tiller.

On another day, I was using a chainsaw to cut down some buckthorn and that same buck was within 5 feet of me eating the leaves on the trees I just cut down. Again completely unafraid.

I put up a small net around the perimeter a few days before I put my plants in and they knocked it over, tore the net, and bent the poles. There wasn’t even anything in the garden! And to top it all off, there were several fresh piles of poop.

So I put in 8 ft. T poles every 4 feet around the perimeter, doubled up the net, secured it at the top and the bottom, and they haven’t gotten in yet (although I watched one of them biting at it). Unfortunately the neighbors are feeding these deer, so they have almost no fear of people.

The role of a district court judge is to do two things:

1. Apply existing precedent to individual cases to the greatest extent possible.
2. Set new precedent only when absolutely necessary because the facts of the case don’t align well to existing precedent.

Cannon has basically decided to do the exact opposite of these two rules by pretending that the facts of this case are so incredibly unprecedented that she has to throw out the rulebook and set new precedents on everything.

Literally the only unusual thing about this case is that the defendant, a private citizen who currently gets free government security protection for the rest of his life, used to be a president. That’s it. Everything else about this case is straightforward obstruction of justice and willful retention of national security information.

“Nah, your fingernails don’t need a trim. If she can’t handle your adult man’s untrimmed fingernails inside her, she does not deserve to have sex with you.”

Hair that’s long and overgrown can cause problems just like long fingernails can cause problems. Keeping them trimmed so they don’t is just being considerate of your partner.

If you want to understand how incredible NYC’s water system is, watch this Wendover video. It blew my mind.

Of course, shitty landlords with old pipes ruins it for a lot of people, but the hard part is done.

https://youtu.be/IDLkOWW0_xg

https://www.axios.com/2024/01/17/americans-are-actually-pretty-happy-with-their-finances

I get a lot of people are struggling, but you can’t claim that the average person isn’t doing well when 63% of Americans rate their financial situation as “good” or “very good.”

But that’s not what TypeScript does. The joke in the meme doesn’t really even make sense.

A better analogy would be you have a basket that’s explicitly labeled “Fruit” and TypeScript complains if you try to put laundry detergent in it because you said it’s supposed to be a basket of fruit.

This meme was clearly made by someone who doesn’t use or understand TypeScript.

I prefer just calling everything I eat the flesh of whatever it came from. Tomato? Flesh. Lettuce? Flesh. People? Flesh.

What if you soak them in high fructose corn syrup first?

Rattlesnakes and alligators (and non-unionized automobile manufacturing facilities)

Biden said he saw the pictures.

https://www.timesofisrael.com/liveblog_entry/meeting-with-jewish-leaders-biden-confirms-reports-that-hamas-beheaded-israeli-children/

“Allegably”

“Howdy” for me. I’m from and live in the Northeast.

Started saying it ironically on work calls to break up the monotony of saying “Hey” when the host joined the meeting and said hello. It was pretty much just a joke at first. Now it’s about 50% of what I say in response to someone joining the meeting saying hello.

Honestly, I kind of like it. It’s folksy, friendly, simple, and informal. It’s slipped out a couple of times when guests arrive at a family party and are walking in the door and saying their hellos, but it’s mostly relegated to work meetings.

A few of my coworkers have even started doing it occasionally, so it seems like it’s catching on.

Just to reinforce your point, the difference between a cheap running shoe and an expensive running shoe is incredible. When I first started running a few years ago, I was using a very old pair of running shoes I’ve had for a long time. I’ve since been sticking with the New Balance Fresh Foam X 880s (because I have very wide feet and NB seems like the only brand that actually makes their best running shoes in 4E) and it’s like running on a cloud.

And then there’s also the Garmin watch that cost $300 (that I’m now stupidly considering upgrading to the new $600 Forerunner 965), the $120 HRM Pro chest strap, the $3000 Nordic Track x22i for indoor runs I got lightly used on Craigslist for a steal at $900, etc.

And then there’s the races where you’re spending $40, $50, $100+ depending on whether it’s a 5K or 10K or half-marathon. And good running clothes are pricey too.

While I agree with you, and I do dearly love garlic, I feel obligated to give you a word of caution:

If you eat too much roasted garlic, for the next 24-48 hours, every room you enter will smell like garlic, your sweat will smell like garlic, your farts (and there will be many) will smell like garlic, and your poop will smell like garlic. It will not be a pleasant experience.

Don’t ask me how I know this.

I noticed Google also changed Maps recently for multi-stop directions so it only calculates routes once you’ve added all the stops instead of after adding each stop. The only rationale I could think of for doing that would be to reduce computation costs.

Seems like they’re going around and trimming compute and network costs wherever they can without significantly impacting user experience.

The short answer is that it’s ultimately down to the number 43 (the number of protons technetium has) and the number of neutrons that could potentially form stable isotopes being atomically weird numbers.

The picture below shows relative stabilities of isotopes of different elements. N represents the number of neutrons, Z represents the number of protons. As a starting rule, moving above or below the N=Z line (creating an excess of protons or an excess of neutrons) tends to decrease overall stability.

You can see for lower atomic numbers, the most stable isotopes closely follow N=Z because protons and neutrons “balance” each other in the nucleus. But as you increase the atomic number (and therefore the number of protons), the protons begin to repel each other more strongly, which means additional neutrons are needed to make the nucleus stable. This is why the “line of stability” (the line of dark red “stable” elements) increases above the N=Z line as you increase the atomic number. Deviation from this line means an atom is less “beta stable” (and therefore more likely to beta-decay).

There are certain “magic” numbers of protons and neutrons that are more stable than others because they comprise a full shell. These occur at 2, 8, 20, 28, 50, 82, and 126. This means nuclei that have (or are very close to) one of these numbers of protons, or neutrons, or protons + neutrons, are inherently more stable. If you look at the other stable isotopes on the graph, you would expect a stable isotope of technetium would need around 55 neutrons to follow the line of stability.

As it turns out, the combinations of 43 protons and 55 (± a few) neutrons just can’t form a stable enough configuration to not beta-decay.

Centrism is, by definition, fence sitting. Someone who is a centrist will often reach a conclusion along the lines of “the left is too extreme, the right is too extreme, therefore whatever is halfway between them must be right.”

This obviously causes some problems. Someone on the left might say gay people are human beings who deserve dignity and respect, while someone on the right might say gay people are icky and unnatural and shouldn’t exist. A centrist would naturally conclude that both positions are too extreme, so how about we treat gay people with dignity as long as they stay in the closet and pretend they aren’t gay? Then everyone’s happy!

Centrists are like libertarians. Their ideology sounds really enlightened and appealing, but in practice, it usually ends up screwing over a lot of people, especially the most vulnerable, and benefiting social conservatives and the wealthy.