Am I going crazy? One toothbrush for every person. I’m a monogamuggle, and I don’t even share a toothbrush regularly with my wife. If you insist on the counter being tidy, put them in a drawer. Also prevents aerosolized fecal matter from getting on the toothbrush head.
That’s a deep cut reference. 👏
My brother is a crank because ChatGPT enables him.
The way that arsonist was able to melt the weird pointy top into something more appealing was really a thing of beauty.
Bouba > Kiki
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 nonnegative 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 🍍?
Twilight 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.)
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.
It turns out, that for the values we are talking about here, it actually more or less does! A lemon has a pH of around 2.5, while “Flow” has an advertised pH of 8.1. This means roughly that to neutralize 1L of this water you need approximately 0.4mL of lemon juice or about 8 drops/half a gram. It’s hard to tell how much a “spritz” is intended to be, but a single lemon contains about 60mL of juice, so this represents about 0.67% of the total juice inside.
It’s a surprising consequence of using a logarithmic scale for pH.