Oh! My bad! I completely missed that the functions were continuous (it isn’t required for 🍊 to be a metric)
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Cake day: June 14th, 2023
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Careful ⚠️ there is not guaranteed to be an element such that |🍎(x) - 🍇(x)| is maximized. Consider 🍎 (x) = x if x < 3, 0 otherwise. Let 🍇 (x) = 0, and let the domain be [0, 4]. Clearly, the sup(|🍎 (x) - 🍇 (x)| : x ∈ [0, 4]) = 3, but there is no concrete value of x that will return this result. If you wish to demonstrate this in this manner, you will need to introduce an 🐘 > 0 and do some pedantic limit work.
Anyway, to prove this is a metric we must prove that it satisfies the 4 laws of metrics.
1. The distance from a point to itself is zero. 🍊 (🍎, 🍎) = 0
This can be accomplished by simply observing that |🍎 (x) - 🍎 (x)| = 0 ∀x ∈ [a,b], so its sup = 0.
2. The distance between any two distinct points is non-negative.
If 🍎 ≠ 🍌, then ∃x ∈ [a,b] such that 🍎 (x) ≠ 🍌 (x). Thus for this point |🍎 (x) - 🍌 (x)| > 0 and the sup > 0.
3. 🍊 (🍎, 🍌) = 🍊 (🍌, 🍎) ∀(🍎, 🍌) in our space of functions.
Again, we must simply apply the definition of 🍊 observing that ∀x ∈ [a,b] |🍎 (x) - 🍌 (x)| = |🍌 (x) - 🍎 (x)|, and the sup of two equal sets is equal.
4. Triangle inequality, for any triple of functions (🍎, 🍌, 🍇), 🍊 (🍎, 🍌) + 🍊 (🍌, 🍇) ≥ 🍊 (🍎, 🍇)
For any (🐁, 🐈, 🐕) ∈ ℝ³ it is well known that |🐁 - 🐕| ≤ |🐁 - 🐈| + |🐈 - 🐕|, (triangle inequality of absolute values).
Further, for any two functions 🍍, 🍑 we have sup({🍍 (x) : x ∈ [a, b]}) + sup({🍑 (x) : x ∈ [a, b]}) ≥ sup({🍍 (x) + 🍑 (x) : x ∈ [a, b]})
Letting 🍍 (x) = |🍎 (x) - 🍌 (x)|, and 🍑 (x) = |🍌 (x) - 🍇 (x)|, we have the following chain of implications:
🍊 (🍎, 🍌) + 🍊 (🍌, 🍇) = sup(🍍 (x) : x ∈ [a, b]}) + sup({🍑 (x) : x ∈ [a, b]}) ≥ sup({🍍 (x) + 🍑 (x) : x ∈ [a, b]}) ≥ sup({) = 🍊 (🍎, 🍇)
Taking the far left and far right side of this chain we have our triangles inequality that we seek.
Because 🍊 satisfies all four requirements it is a metric. QED.
QED stands for 👸⚡💎, naturally
What happened to 🍇 and 🍍?
9·20 days agobut can I say he’s wrong? I don’t know.
Not a cult. Not a cult. Not a cult. Not a cult.
4·27 days agoAnakin brought balance to the force by slaughtering all of the Jedi.
Before, thousands of Jedi, like 4(?) sith.
After, 2 Jedi, 2 sith. Perfectly balanced.
4·28 days agoGmail data gets used in LLM training. I wonder how Gemini 2.5 would auto complete “The code to the nuclear football is”…
Says the guy insinuating context to justify this attack, and accusing the woman attacked of lying, despite the fact that she was fired for not reporting the attack to a manager quickly enough?
At this point, you’re just embarrassing yourself. Lemmy is still too small for everyone here not to see through this weak ass bait.
Are you asserting that she is lying about being accosted by a man for entering the women’s bathroom?
Because if you aren’t, then I would be very interested to hear what “more that happened” could possibly justify his actions.
Johnny Mnemonic
2·1 month agoTwilight princess got a HD remaster though.
Having played all of the 2d Metroids, Super Metroid still holds up very well, even compared to the newer games. There’s less direction than what you might be used to though. Newer entries in the series tend to try to funnel you places. But if you are simply concerned about the gameplay being clunky, don’t be.
Super Metroid way ahead of its time, and the controls are extremely responsive and tight. It’s one of the reasons it’s such a popular speed game. It’s just fun to play. While basic controls are serviceable, there are many tricks you find yourself learning about as you play the game, which you just have access to, that give the movement system quite a bit of depth. (For hints, let the attract move run at the beginning of the game.)
Why is “gives free tech support,” an expectation of being a good person? I spent 7 years of my life doing tech support professionally.
a) I never want to do it again, because honestly fuck computers, but b) If I have to, I’m certainly not going to do it unless I already like you or you are paying me.
Figure your own shit out. I have a life to live and I don’t have infinite free time and energy to help you unfuck whatever stupid bullshit happened to your computer. Especially if you’re being entitled about it.
I mean, by pushing conservative media narratives and moving the Overton window to the right, you could argue that Hallmark is in part responsible for our illegal ICE deportations to El Salvadorian torture prisons, the rise in hate crimes against transpeople, and our future war with Iran.
But maybe an extra white lady got killed too.
Are you kidding? Do you not remember? That is exactly what a pokemon journey is for! Now put on a baseball cap, grab your Bulbasaur, and get out there and be the very best like no one ever was.
I googled it for you.
https://en.wikipedia.org/wiki/XX_male_syndrome
In 90 percent of these individuals, the syndrome is caused by the Y chromosome’s SRY gene, which triggers male reproductive development, being atypically included in the crossing over of genetic information that takes place between the pseudoautosomal regions of the X and Y chromosomes during meiosis in the father.[2][7] When the X with the SRY gene combines with a normal X from the mother during fertilization, the result is an XX genetic male. Less common are SRY-negative individuals, those who are genetically females, which can be caused by a mutation in an autosomal or X chromosomal gene.[2] The masculinization of XX males is variable.
Same tbh. Framework just works. And they do contribute back, just perhaps not as much specifically to Linux. Open source hardware is so incredibly valuable and important and rare. Honestly, if I had to choose only based on how much is contributed back, I’d still pick Framework.
3·2 months agoI’m currently working on a government funded project to develop a robot to locate nuclear contamination in soil (for cleaning up the Hartford and Savannah River sites, where we used to make nuclear weapons). The idea being that we use robots to perform these surveys rather than handheld detectors.
My recommendation though, is focus only on one thing. Having two degrees has not made me particularly marketable, it is certainly unique, but HR doesn’t actually seem to give much of a shit. Instead, it’s much better to focus on one thing, get a Masters or PhD in it (double degrees also suck for this as well, because you don’t have time for research and publishing when you’re graduating with 195 credit hours taken out of 128 required, so even if you have a good GPA it’s hard to get into grad school).
Bouba > Kiki