• 2 Posts
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Joined 3 years ago
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Cake day: June 14th, 2023

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  • OmnipotentEntity@beehaw.orgtoScience Memes@mander.xyzAha!
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    4 days ago

    If you floss regularly your gums won’t bleed, source: me. My gums never bleed at the dentist, but they used to when I sucked more at dental self-care.

    For the X-ray example, think about it this way: the doctor is like a bartender. One drink isn’t going to hurt you. The bartender can definitely serve you one drink. But if the bartender had to drink a part of a drink every time they served someone, that would become pretty dangerous for them indeed.












  • 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.








  • OmnipotentEntity@beehaw.orgto196@lemmy.blahaj.zoneRule
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    5 months ago

    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({🍎 (x) - 🍇 (x)| : x ∈ [a, b]) = 🍊 (🍎, 🍇)

    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