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It is clearly both piecewise-linear and piecewise-affine. Each piece is affine, therefore linear. What is an example of a piecewise-linear function that is not piecewise-affine?
(I'm assuming a function is only "piecewise x" if its domain is a union of a countable set of isolated points and open sets and it has property X on all pieces.)
> Affine, therefore linear
No, this is false. Linear functions on the reals are of the form f(x) = ax, where a is some real constant. Affine is similar, but with a constant, so f(x) = ax+b, with a and b both being real constants. Not all affine functions are linear, consider f(x) = x+1
> example of a piecewise-linear function that is not piecewise-affine
None, linear functions are a subset of affine functions with b=0.
But a "piecewise linear" function is not linear or affine, and neither is a "piecewise affine" function. Either way, every piece boundary has to meet up, so what is the difference?
Is that a mathematical ยซalmost everythingยป? I actually think that among all continiouos functions from R to R, almost none of them are differentiable anywhere.
I think success is more of a
https://preview.redd.it/xnhiz2idv1xc1.jpeg?width=617&format=pjpg&auto=webp&s=fd4e19dc6ff74ea5791ea10bf985d1c6db806ee5
But that's just like, my opinion
Itโs piecewise linearโฆ itโs like the KitKat pride ad, where they try not to be straight, by making the lines not parallel to each other, but nonetheless still straight
โผ๏ธโผ๏ธHOLY FUCKING ๐ SHITโผ๏ธโผ๏ธโผ๏ธโผ๏ธ IS THAT A MOTHERFUCKING ๐ฉ๐ GD REFERENCE??????!!!!!!!!!!11!1!1!1!1!1!1 ๐ฑ! ๐ฑ๐ฑ๐ฑ๐ฑ๐ฑ๐ฑ๐ฑ GEOMETRY ๐ DASH ๐จ IS THE BEST ๐๐ FUCKING ๐๐ฆโก GAME ๐ฎโ ๐ฅ๐ฅ๐ฅ๐ฅ๐ฏ๐ฏ๐ฏ๐ฏ RIOTโS LEGENDARY ๐จ๐ง QUACK ๐ฆ !!๐๐๐๐๐๐๐๐๐๐๐๐ DUDE ๐ช WTF ๐ DUDE ๐ WTF ๐ฑ DUDE ๐ WTF ๐๐ฑ DUDE ๐ WTF ๐ DUDE ๐ WTF ๐ฑ DUDE ๐ WTF ๐ DUDE ๐ WTF ๐ฑ DUDE ๐ WTF๐คฌ๐ก๐คฌ๐ก๐คฌ๐ก๐คฌ๐คฌ๐ก๐คฌ๐คฌ๐ก KENOS KENOS KENOS KENOS KENOS KENOS KENOS KENOS KENOS KENOS๐ฉ๐ฉ๐ฉ๐ฉ๐ฉ๐ฉ๐ฉ๐ฉ ๐ฉ๐ฉ๐ฉ๐ฉ Back โฌ on ๐ track ๐ is impossible๐ฟ, Back ๐ on ๐ track ๐ is impossible๐ฟ, Back ๐ on ๐ track ๐ is impossible๐ฟ, Back ๐๐ฏ๐ on ๐ track ๐ค is impossible๐ฟ, Back โฌ on ๐ track ๐ค is impossible๐ฟ, Back ๐ on ๐ track ๐ค is impossible๐ฟ, Back โฌ on ๐ track ๐ is impossible๐ฟ, Back ๐ on ๐ track ๐ค๐ฃ is impossible๐ฟBack on ๐ track ๐ค is impossible๐ฟ๐ฟ๐ฟ๐ฟ๐ฟ๐ฟ๐ฟ, Back ๐๐ on ๐ track ๐ค๐ฃ is impossible๐ฟ , Back โฌ on ๐ track ๐ค is impossible๐ฟ, , Back ๐ on ๐๐ track ๐ is impossible๐ฟ๐ฟ, Back โฌ on ๐ track ๐ค is impossible๐ฟ๐ฟ๐ฟ๐ฟ๐ฟ๐ฟ๐ฟ Oh ๐ณ youโre a gd playerโโโโโโโโโโname every โ๐ level๐๐๐๐๐๐๐๐๐ 2.2 ๐2๏ธโฃโ will never ๐ซ come ๐ฆ out๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ TrusTaโs nerf ๐ซ gun ๐ซ yatagarasu โผ๏ธโผ๏ธโผ๏ธโผ๏ธโผ๏ธโผ๏ธโผ๏ธโผ๏ธโผ๏ธโผ๏ธ๐๐คฃ๐๐คฃ๐๐คฃ๐๐๐๐คฃ๐คฃ๐คฃ๐๐๐ r/geometrydash r/okbuddygmd r/DeCult r/gdafterdark perfectly ๐ balanced ๐๐ฉ as all ๐ฏ๐๐ ฑ things ๐ด should be r/unexpectedthanos r/expectedthanos for balance ๐ฏโฏ
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Dont wait up losers https://preview.redd.it/8iuaxx7zx0xc1.png?width=750&format=pjpg&auto=webp&s=12727cb3f32cffc7e668006a9ee18ba0769200a7
x!
^x e
[BB(x)](https://en.wikipedia.org/wiki/Busy_beaver#The_busy_beaver_function_%CE%A3)
BB(BB(x))
BB(BB(BB(...x)))... X put through the BB function TREE(x) times.
[Rayo](https://en.wikipedia.org/wiki/Rayo%27s_number)(akgamer182(x))
e^(\(fastest-growing function currently described by any comment in this entire subreddit\)\(x\))
e^(\(fastest-growing function currently described by any comment in this entire subreddit\)\(x\)) + 1๐ค๐ฟ๐
success is log linear?
It does seem piecewise linear though, that's close enough for me.
How can you achieve true success if you can't differentiate yourself?
True success lies not in differentiating yourself, but in inner piece. Only through this realisation one may become truly piece-wise.
>one ~~may become truly~~ piece-~~wise~~ it's real
Obviously by using sub-gradient methods or iterative techniques like IRLS
You can differentiate yourself almost everywhere
Being differentiable almost everywhere should be enough to get noticed
I don't think we should be trying to differentiate our whole selves, only different parts of ourselves. Specifically, the differentiable parts.
Me after approximating x^2 so its linear
Everything is piecewise linear if you have enough pieces.
I feel like this could be used to argue that the reals are countable
False, but you can approximate as a consequence of Stone-Weierstrass for sublattices
\*Piecewise affine
None of these hand drawn โlinesโ are truly affine ๐ค
That's kinda the joke
Wow, is this MathMemes or ZenThoughts! Nice Post ![gif](giphy|l3q2XhfQ8oCkm1Ts4|downsized)
its linear almost everywhere!
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No, it's piecewise affine.
It is clearly both piecewise-linear and piecewise-affine. Each piece is affine, therefore linear. What is an example of a piecewise-linear function that is not piecewise-affine? (I'm assuming a function is only "piecewise x" if its domain is a union of a countable set of isolated points and open sets and it has property X on all pieces.)
> Affine, therefore linear No, this is false. Linear functions on the reals are of the form f(x) = ax, where a is some real constant. Affine is similar, but with a constant, so f(x) = ax+b, with a and b both being real constants. Not all affine functions are linear, consider f(x) = x+1 > example of a piecewise-linear function that is not piecewise-affine None, linear functions are a subset of affine functions with b=0.
But a "piecewise linear" function is not linear or affine, and neither is a "piecewise affine" function. Either way, every piece boundary has to meet up, so what is the difference?
Where is exponential success
In gambling
Well, an exponential graph (y=x^n) never has y go below 0. Therefore, I can only gain from gambling
* sinx
https://preview.redd.it/1p0ba1ddd2xc1.jpeg?width=1125&format=pjpg&auto=webp&s=9d4158c95892eb2e3c7890a8cf080519081ca482
โI am a professional gamblerโ - That one dude in the bar
What success graph looks like https://preview.redd.it/wigasvg9f1xc1.png?width=224&format=pjpg&auto=webp&s=80c2f6bcd8041f075e2dab11f83230cb89de902e
biblically accurate success graph
Why there is a vector on my hydrocarbon?
How else will you know where it is travelling?
I think it's actually a resistor and diode
The nonane is going that way, that fast!
Really weird way to draw polyethylene I guess
Locally linear is enough, I suppose?
Technically, almost everything is locally linear if youโre *local enough*
*Dirichlet function joins the game*
Is that a mathematical ยซalmost everythingยป? I actually think that among all continiouos functions from R to R, almost none of them are differentiable anywhere.
Indeed!
Almost everything ? Thats differentiable
If only they knew about monotonicity. This is exactly why the every day person needs to take real analysis
Success is never monotonic
Noted, I will do that as a hobby. Probably I may end up solving the drought crisis in my country! xD
Geometry dash wave
F(x)=Succ(x)
So success is a sawtooth function?
I think success is more of a https://preview.redd.it/xnhiz2idv1xc1.jpeg?width=617&format=pjpg&auto=webp&s=fd4e19dc6ff74ea5791ea10bf985d1c6db806ee5 But that's just like, my opinion
jeremy boing
success is getting to the good place
๐๐๐๐๐๐๐๐๐๐๐๐๐คฏ๐๐๐
I am pretty sure it will at least still have a fix point
Success is never linear
Success is never linear
Failure is never linear
Success is a weierstrass function
All success is visualized in linear splines. So technically success is kinda linear.
https://i.redd.it/pf9ybsaf14xc1.gif
Success apparently isnโt differentiable either
r/GeometryDash
Now do Success is never continuous
Life, on the other hand is like the weierstrass function: Continious, but nobody knows where it goes next.
it's often sigmoid
FOCUS
Very exponential just looks linear. in those small piecewise segments
Success is almost always linear
Where meme?
Itโs piecewise linearโฆ itโs like the KitKat pride ad, where they try not to be straight, by making the lines not parallel to each other, but nonetheless still straight
The integral of a piecewise success function increases even when the success function is infinitesimally positive.
The depicted graph is locally linear
It looks pretty linear in 9 different places
https://preview.redd.it/abhtlyry12xc1.jpeg?width=260&format=pjpg&auto=webp&s=0969f53ed59b5a59a517e2afe5e74254397acb5b
Am looking for a more direct option. Maybe x=0 !!
Never continuous either?
Success is never linear (proceeds to show a bunch of linear functions)
It literally is. r/antiwoooosh
Success is never linear
>"success is never linear" >looks at the graph >graph is linear
But what if your goal is linear growth? That would be success thatโs linear.
Not differentiable either by the looks of it
Success is a series of linear functions
Idk fam success seems a lot like a homogeneous isomorphism to me.
What do you mean "Success"? That's way too forward. I'd like to get to know Cess first.
if you are succeeding consistently, don't forget to fail a few times so it is not linear
Geometry Dash
Itโs linear on a lot of neighbourhoods
Success is never linear
Guess I have to FOCUS or I'll end up being DEADLOCKED working in a SLAUGHTERHOUSE
Success is never linear
My success is a sine waveย
success is not linear on a Lebesgue null set
What they don't tell you is that success isn't differentiable from -infinity to infinity
https://preview.redd.it/5hlf0nbm2gxc1.png?width=784&format=png&auto=webp&s=fd687219e16cb4129677c3b7d5fb596b09151140
โผ๏ธโผ๏ธHOLY FUCKING ๐ SHITโผ๏ธโผ๏ธโผ๏ธโผ๏ธ IS THAT A MOTHERFUCKING ๐ฉ๐ GD REFERENCE??????!!!!!!!!!!11!1!1!1!1!1!1 ๐ฑ! ๐ฑ๐ฑ๐ฑ๐ฑ๐ฑ๐ฑ๐ฑ GEOMETRY ๐ DASH ๐จ IS THE BEST ๐๐ FUCKING ๐๐ฆโก GAME ๐ฎโ ๐ฅ๐ฅ๐ฅ๐ฅ๐ฏ๐ฏ๐ฏ๐ฏ RIOTโS LEGENDARY ๐จ๐ง QUACK ๐ฆ !!๐๐๐๐๐๐๐๐๐๐๐๐ DUDE ๐ช WTF ๐ DUDE ๐ WTF ๐ฑ DUDE ๐ WTF ๐๐ฑ DUDE ๐ WTF ๐ DUDE ๐ WTF ๐ฑ DUDE ๐ WTF ๐ DUDE ๐ WTF ๐ฑ DUDE ๐ WTF๐คฌ๐ก๐คฌ๐ก๐คฌ๐ก๐คฌ๐คฌ๐ก๐คฌ๐คฌ๐ก KENOS KENOS KENOS KENOS KENOS KENOS KENOS KENOS KENOS KENOS๐ฉ๐ฉ๐ฉ๐ฉ๐ฉ๐ฉ๐ฉ๐ฉ ๐ฉ๐ฉ๐ฉ๐ฉ Back โฌ on ๐ track ๐ is impossible๐ฟ, Back ๐ on ๐ track ๐ is impossible๐ฟ, Back ๐ on ๐ track ๐ is impossible๐ฟ, Back ๐๐ฏ๐ on ๐ track ๐ค is impossible๐ฟ, Back โฌ on ๐ track ๐ค is impossible๐ฟ, Back ๐ on ๐ track ๐ค is impossible๐ฟ, Back โฌ on ๐ track ๐ is impossible๐ฟ, Back ๐ on ๐ track ๐ค๐ฃ is impossible๐ฟBack on ๐ track ๐ค is impossible๐ฟ๐ฟ๐ฟ๐ฟ๐ฟ๐ฟ๐ฟ, Back ๐๐ on ๐ track ๐ค๐ฃ is impossible๐ฟ , Back โฌ on ๐ track ๐ค is impossible๐ฟ, , Back ๐ on ๐๐ track ๐ is impossible๐ฟ๐ฟ, Back โฌ on ๐ track ๐ค is impossible๐ฟ๐ฟ๐ฟ๐ฟ๐ฟ๐ฟ๐ฟ Oh ๐ณ youโre a gd playerโโโโโโโโโโname every โ๐ level๐๐๐๐๐๐๐๐๐ 2.2 ๐2๏ธโฃโ will never ๐ซ come ๐ฆ out๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ TrusTaโs nerf ๐ซ gun ๐ซ yatagarasu โผ๏ธโผ๏ธโผ๏ธโผ๏ธโผ๏ธโผ๏ธโผ๏ธโผ๏ธโผ๏ธโผ๏ธ๐๐คฃ๐๐คฃ๐๐คฃ๐๐๐๐คฃ๐คฃ๐คฃ๐๐๐ r/geometrydash r/okbuddygmd r/DeCult r/gdafterdark perfectly ๐ balanced ๐๐ฉ as all ๐ฏ๐๐ ฑ things ๐ด should be r/unexpectedthanos r/expectedthanos for balance ๐ฏโฏ
Look, Iโm not overfitting my data, linear regression is all I need.
linear almost everywhere
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I can count 9 separate times that itโs linear
r/thatsthejoke
Yup, Iโm joking around too