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Notes -
LaTeX also doesn't interpret repeated * symbols as a request to hide them both and italicize the text between them. ;-)
Oof, yes. Fixed.
That one's bitten me too many times before, but these days using Unicode for x·y·z when I want an explicit symbol works well and is almost second nature, when I'm thinking in "math mode". If I'm thinking in "programming mode" then I default to
x*y*zbut the whole expression is inside backticks and markdown doesn't ruin it.What markdown still wrecks for me is the use of "~40" to indicate that the number is a loose approximation, which then sometimes turns into a big strikethrough if I use it a second time. Unicode gives us ≈, but that doesn't feel right to me when there's nothing to the left of it.
I like your preferred method of analysis, BTW. It reminds me of the old argument that the US should be expressing vehicle efficiency in gallons per mile (or per 1000 miles, whatever) rather than in miles per gallon, because the latter leads us to overestimate how large the additional savings are when we further improve already-high-efficiency vehicles and to underestimate how important improvements are for the remaining gas guzzlers.
Oh man, approximately still gets me every time. I just write it, then when I got to paste it in, I see that it breaks, then I consider whether I want to spend a few minutes re-figuring-out what I want to do. I've given up in some comments not too long ago; pretty sure I just wrote "\approx", not caring. I'll be saving @ToaKraka's comment, and hopefully I remember I have it the next time it happens.
And indeed, at the time I came up with this way of thinking about it (I'd say about a decade ago), I was thinking about the debate on mpg/gpXm. I almost mentioned that here, because, yeah, a lot of people think in terms of having a fixed number of miles they're traveling, but don't intuitively grok 1/x relations. This speeding analysis is at least linear in distance, but it still has a 1/x relation, in a way. Yes, it's actually 1/x^2, but I guess what I'm kinda thinking is that one can lean on the 60min/1hr conversion, you have (d/r)
*(60/r), and almost do it in two stages in your mind. If your nominal speed is 70, then you still have a d/r relation, but it's slightly modified by a 60/70, and I at least have a bit of an intuition as to how far off that's going to make my approximation, rather than having to just brute calculate the whole thing, actually thinking about the squared term.More options
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Fun fact: You can use the code charts (or software like BabelMap) to find official alternatives for problematic characters.
Alternatives to 007E ~ tilde (HTML named character reference
Tilde) (not including combining characters):02DC ˜ small tilde (HTML named character reference
tilde)2053 ⁓ swung dash
223C ∼ tilde operator (HTML named character reference
sim)2E1B ⸛ tilde with ring above
2E2F ⸯ vertical tilde
301C 〜 wave dash
FF5E ~ fullwidth tilde
Obviously, HTML named character references are a lot easier to remember than hexadecimal representations, so & sim; (without the space) probably is the best alternative for use on this website.
How do you use the hexadecimal ones?
& #x223c; (without the space) = & sim; (without the space) = ∼
HTML documentation
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Oh, wow, that's a good idea. ~ is actually a better "pay attention, this is not a blurry minus sign, this is approximation" character, at least on my screen.
I'm a big X Compose Key fan, especially with custom sequences. Need the real numbers?
Win, m, b, R(mnemonic "math bold R") gives me ℝ. Defining the square function x↦x² with "bar arrow" notation? My "Bar arrow" isWin, |, >, and "squared" isWin, ^, 2. I'm already usingWin,for ≈ ... but,Win, b, ~should work for a "bold" tilde, if I could ever remember to use it.More options
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