#mattsamuels

[thebiggaylion]

Eric Prydz @ EDC Orlando 2015 (Part 1 of 2)

Hello again, everyone!  Orlando is still here!  I say that because of Hurricane Irma, having just came through between last week’s #ThrowbackThursday and today.  I haven’t been over by Tinker Field yet to make sure it’s still intact, but considering the baseball diamond was taken down, and all that’s over there is a few walking paths and maybe some light posts, I don’t anticipate any “real” damage.  Whatever it may have, I’m sure things will be ready for November!  Speaking of storm-related incidents, you may notice this is being posted on Friday, not Thursday... well, that’s because the guy who’s behind The Big Gay Lion lost power yesterday during a storm.  Not really related to Irma, but I’m sure the power lines and such around where he lives must be a bit strained heh.  Power outages aren’t really interesting, BUT I wasn’t smart about saving this post frequently like I normally am... and I lost it all haha, so I had to start over today!  Maybe I should call this one #FlashbackFriday?  Oh, honey, by the way... it’s a BIG OL’ POST, for real this week!  This here’s part one, obvi~!  Part two is over there.

I’ve been looking forward to attending an Eric Prydz show for a while, but I’ll be honest:  I didn’t anticipate it being in a festival setting.  I like getting a little (read:  A LOT) turnt at EDC Orlando, and his flavor of house didn’t strike me as “perfect” for this venue, let alone Kinetic Field (even though, yes, he is house, and that’s where house lives at EDC).  However, I wasn’t disappointed by any means!  The only part of the performance that was disappointing was this thoroughly obnoxious person who pushed up next to me and kept swaying back and forth, bumping into me repeatedly and being otherwise distracting.  Sure, PLUR and all, and I get that... but don’t be a nuisance, man!  Anyway, if you see my camera jerk, it’s because dude (on my right) hit my arm--again.  If you hear any vocalizations that clearly aren’t coming from the speakers, that’s also probably him, too haha.

YouTube | Facebook | Instagram What a great song to dust off and play a mix/cover of!  There was lots of underwater-esque visuals during his set, for the Empire of the Sea interstitial had just played before his set.  Those bubble chains and tentacles are something that stuck with me whenever I reminisce about this performance. Matt Samuels feat. For The Masses - Enjoy The Silence https://www.youtube.com/watch?v=fKr4zf9Z92I

YouTube | Facebook | Instagram These visuals stick out a lot for me, too.  Insomniac knows how to theme their CGI, for sure.  In what was one of the only easily recognizable drops in the whole performance, the techs were ready to accent it properly! Popof - Serenity (Noob Remix) https://soundcloud.com/form-music/popof-serenity-noob-remix-6-years-of-form-music-2009-2015

YouTube | Facebook | Instagram I managed to catch a lot of special effects in these videos, it seems!  I also noticed that all of these videos make it seem I’m much closer than I actually am heh.  I’m probably 50 feet or so from the front rails, FYI.  Also, apparently this track is unreleased, so forgive the “who is that guy?” link below haha Cirez D - Metropolitan (ID) https://soundcloud.com/gustav-granath/cirez-d-metropolitan-id

YouTube | Facebook | Instagram R.I.P. Vine.  Man, I do love me some lasers, don’t I?  A flood of classic green lasers like these above will surely hold my attention during any performance. Dusty Kid - Tsunamy https://soundcloud.com/juju-hardstyle/dusty-kid-tsunamy

YouTube | Facebook | Instagram I do like it when an artist brings their own visuals, but sometimes if Insomniac is given free reign on what to display, it comes together much more cohesively, don’t ya think?  Empire of the Sea indeed! Dusty Kid - Tsunamy https://soundcloud.com/juju-hardstyle/dusty-kid-tsunamy

Remember, this is only half of what you could fill your eyes and ears with!  To see it all at once, go here, but since you��re already at part one now, I can imagine you’ll be looking for part two instead.

Carry yourself on to my other socials! Facebook | Tumblr | YouTube | Instagram | Twitter | Web

[mathematicianadda]

Finding $f$ such that $f(f(f(f...(x)))) = x$

I would like to find the set of continuous functions $f_n(x)$, where $f_n(x):\mathbb{R}\to \mathbb{R}$ satisfies $$f_n(f_n(f_n(f_n...(x)))) = x$$ where there are $n$ iterations of $f(x)$. For example $f_1(x)$ would be the solution to $f_1(x)=x$. $f_2(x)$ would be the solution to $f_2(f_2(x)) = x$.

For $f_1(x)$, the only solution is $f_1(x)=x$. For $f_2(x)$, the solutions are involutions.

For $f_3(x)$, the only answer is $f_3(x)=x$. For all other $f_n(x)$, one solution is $f_n(x) = x$.

My question: For $n \ge 3$, is $f_n(x) = x$ the only solution? If not, what are the solutions?

Edit: @MattSamuel said that any involution works for an even $n$. This is because $f_n(f_n(x))$ can be replaced with $x$. For example, $$f_2(f_2(f_2(f_2(f_2(f_2(x)))))) = f_2(f_2(f_2(f_2(x)))) = f_2(f_2(x)) = x$$ However, this does not necessarily mean that involutions are the only set of solutions for $f_{2k}(x)$.

from Hot Weekly Questions - Mathematics Stack Exchange from Blogger https://ift.tt/2LR7o1h