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x^2
—— = x
xProof?
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
x = x^1/2^ * x^1/2^becomes
x = x1/2 * x1/2
Somebody please crop this meme to A4 paper’s aspect ratio
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.
Removed by mod
The other way around you get √
(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
Observe the identities
a / b = a × b^(-1) (A) sqrt(a) = a ^ (1/2) (B) a^b × a^c = a^(b+c) (C) (a^b)^c = a^(b × c) (D)and derive
2 / sqrt(2) = 2 / 2^(1/2) (B) = 2 × [2^(1/2)] ^ (-1) (A) = 2 × 2^(1/2 × (-1)) (D) = 2 × 2^(-1/2) = 2 ^ [1 + (-1 / 2)] (C) = 2 ^ (1/2) = sqrt(2) (B)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.
Wtf is this
Maf
Quick maffs
True but dum maphs
x^2
—— = x
xWell 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.
Yes.
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 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
c/mathmemes
How am I s’posed to root two this?
(Aw, gimme somethin’ I can root two!)
i too remember when i was on 8th grade
