putitoutwithyourbootsted@piefed.social
on 29 Mar 19:25
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Neat breakdown! Can you explain why this line =2^(1+ -1/2) =>2^(-1/2)
shouldn’t it be 2^(1/2) or am I missing something? Second guessing myself here lol
x² - x² = 0 and x - x = 0, then 0 = 0 and uh… again.
JPAKx4@lemmy.blahaj.zone
on 29 Mar 20:22
nextcollapse
If you’re saying two variables are equal, then x=x is valid. The only issue with this is it doesn’t indicate the restriction at x=0. This is a “hole” in the function since anything/0 is undefined. For all other cases the equation holds true.
The dirty little secret is…there is no “true markdown”. There are multiple different implementations of markdown that have been created by different people at different times, all vaguely based on the original not-very-robust definition created by John Gruber with assistance from Aaron Swartz in 2005. But their definition never mentioned superscript at all.
Because of how unrobust it is, in 2014, some people got together to define a robust specification and called it CommonMark. But again, this does not mention superscript.
The closest you’ll find to an “official” specification for the extra bits of markdown that aren’t in the CommonMark spec is probably here. But this is really more attempting to describe extended markdown as it is used on the web at large already. In addition to super- and sub-script, it also deals with tables (which work the same way Reddit does them) and fenced code blocks (the triple backtick method, which Reddit does not support—instead supporting only code blocks via four spaces). Though both fenced and indented code blocks are actually in the CommonMark spec.
Reddit, obviously, is one site that famously implements markdown, and has done for a very long time. On Reddit, superscript is done with a caret before the superscript text, and whitespace after it. Unless you use brackets, in which case the superscript lasts until the closing bracket. e.g. normal^superscript text would make “superscript” superscript, but nothing else. But normal ^(superscript text) would make “superscript text” superscript. But then there’s a second caveat, which is that Reddit supports double (and triple, etc.) superscript. But in these cases, brackets do not work. They unintuitively completely break things.
Lemmy also uses markdown. The Lemmy specification for how to use markdown is located here. You’ll note that it supports both superscript and subscript, which Reddit does not. It does both of these according to the method explained in the “markdown guide”. Though there are a few issues with inconsistent parsing of the markdown on lemmy-ui (the default web front-end) and some apps (including Jerboa, the 1st-party app).
The big advantage of the markdown guide method is that it is most similar to how other markdown works. You don’t implicitly close italics on a word with just one asterisk; you need two asterisks—one to open italics, one to close them. Likewise, bold with double asterisks. By using a character to both open and close your super/sub-script, you are making a much clearer and more deliberate intention about what you want, and allowing people to learn things more intuitively, because it all works the same way as each other.
TootSweet@lemmy.world
on 29 Mar 19:38
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This isn’t intuitive to people?
2/sqrt(2) = ( sqrt(2)*sqrt(2) ) / sqrt(2)
Then cancelling out one of the sqrt(2)s in the numerator with the sqrt(2) in the denominator, you’re left with sqrt(2).
I do a lot of toodling around in OpenSCAD, though, and sqrt(2) tends to come up a lot because, you know, Pythagoras and right triangles and all that.
1/sqrt(2) and 0.5 * sqrt(2) both being 0.707 always blows my mind even though it’s basic algebra
ChaoticNeutralCzech@feddit.org
on 29 Mar 22:31
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If you crop the extra white space at the top, this meme has the √2̅:1 (or 2:√2̅) aspect ratio, which I find more pleasing than the “golden ratio”, perhaps because I’m so used to A4 paper
threaded - newest
Wtf is this
Maf
Quick maffs
True but dum maphs
Yes.
x^2
—— = x
x
Well the square root of x times itself gives you x
I had to go through the five stages of grief to fully process your explanation. Thanks for explaining.
What if I told you that it works for any number 𝑥 you replace 2 with? (Except for 0 but still working for 𝐥𝐢𝐦 𝑥→0)
… where x is positive.
Otherwise it has an imaginary component and is complex.
Nope, it still works even then.
NOW I get it. Thanks.
Observe the identities
and derive
Neat breakdown! Can you explain why this line =2^(1+ -1/2) =>2^(-1/2)
shouldn’t it be 2^(1/2) or am I missing something? Second guessing myself here lol
No, that’s a mistake. Incredible how many mistakes one can make in a simple derivation.
Thanks for pointing it out.
All good! Thanks for the very helpful explanation.
i too remember when i was on 8th grade
x^2
—— = x
x
Proof?
ETA: Quick verification.
x² - x² = 0 and x - x = 0, then 0 = 0 and uh… again.
If you’re saying two variables are equal, then x=x is valid. The only issue with this is it doesn’t indicate the restriction at x=0. This is a “hole” in the function since anything/0 is undefined. For all other cases the equation holds true.
So x = x if x ≠ 0 and x ≠ x ≠ 0 if x = 0, got it.
x = x^1/2 * x^1/2
x/ x^1/2 = x^1/2
No need to escape the carets. On Lemmy, superscript is done by placing a caret both before and after the text you want to be superscript. So
becomes
x = x^1/2^ * x^1/2^
is this “true markdown”? What was wrong with “fake markdown” that needed this abomination?
The dirty little secret is…there is no “true markdown”. There are multiple different implementations of markdown that have been created by different people at different times, all vaguely based on the original not-very-robust definition created by John Gruber with assistance from Aaron Swartz in 2005. But their definition never mentioned superscript at all.
Because of how unrobust it is, in 2014, some people got together to define a robust specification and called it CommonMark. But again, this does not mention superscript.
The closest you’ll find to an “official” specification for the extra bits of markdown that aren’t in the CommonMark spec is probably here. But this is really more attempting to describe extended markdown as it is used on the web at large already. In addition to super- and sub-script, it also deals with tables (which work the same way Reddit does them) and fenced code blocks (the triple backtick method, which Reddit does not support—instead supporting only code blocks via four spaces). Though both fenced and indented code blocks are actually in the CommonMark spec.
Reddit, obviously, is one site that famously implements markdown, and has done for a very long time. On Reddit, superscript is done with a caret before the superscript text, and whitespace after it. Unless you use brackets, in which case the superscript lasts until the closing bracket. e.g.
normal^superscript textwould make “superscript” superscript, but nothing else. Butnormal ^(superscript text)would make “superscript text” superscript. But then there’s a second caveat, which is that Reddit supports double (and triple, etc.) superscript. But in these cases, brackets do not work. They unintuitively completely break things.Lemmy also uses markdown. The Lemmy specification for how to use markdown is located here. You’ll note that it supports both superscript and subscript, which Reddit does not. It does both of these according to the method explained in the “markdown guide”. Though there are a few issues with inconsistent parsing of the markdown on lemmy-ui (the default web front-end) and some apps (including Jerboa, the 1st-party app).
The big advantage of the markdown guide method is that it is most similar to how other markdown works. You don’t implicitly close italics on a word with just one asterisk; you need two asterisks—one to open italics, one to close them. Likewise, bold with double asterisks. By using a character to both open and close your super/sub-script, you are making a much clearer and more deliberate intention about what you want, and allowing people to learn things more intuitively, because it all works the same way as each other.
This isn’t intuitive to people?
Then cancelling out one of the
sqrt(2)s in the numerator with thesqrt(2)in the denominator, you’re left withsqrt(2).I do a lot of toodling around in OpenSCAD, though, and
sqrt(2)tends to come up a lot because, you know, Pythagoras and right triangles and all that.Also pops up a lot in basic electrical engineering as the conversion factor between amplitude and RMS value of sine waves
It’s Really simple once you get it, but it allways blows my mind.
1/sqrt(2) and 0.5 * sqrt(2) both being 0.707 always blows my mind even though it’s basic algebra
If you crop the extra white space at the top, this meme has the √2̅:1 (or 2:√2̅) aspect ratio, which I find more pleasing than the “golden ratio”, perhaps because I’m so used to A4 paper
<img alt="" src="https://feddit.org/pictrs/image/ea9741d5-b0fd-4ad1-8343-732a76be439f.webp">
The other way around you get √
<img alt="" src="https://files.catbox.moe/nas0dj.jpg">
(I can’t even draw simple stuff…)
Hard to draw when you’re so busy kissing boys
You like installing arch don’t you, you’re an arch installer aren’t you
Also, i use fedora
How am I s’posed to root two this?
(Aw, gimme somethin’ I can root two!)
c/mathmemes