/sci/ - Science & Math

>>4336118
f(0) = 0
f(x) = 1, where x != 0

(1-t)x+ty

map everything to 1/2!
but I assume you mean a homotopy

>>4336148
also, arctan gives a homeomorphism to an interval (at which point its easy to move it to (0,1). Then combine that with >>4336130 to get a deformation.

>>4336148
>>4336159
Why the fuck would OP want a to show that R is homotopy equivalent to an intervall?! It's much easier and straightforward to just show that it's homeomorphic to an intervall and homotopy equivalence follows by definition. As for the homeomorphism it's easiest to just take
<div class="math">\frac{2x-1}{|2x-1|-(2x-1)^2}</div>
for x!=1/2 and to map 1/2 to 0. It's much more sensible to check that this is indeed a homeomorphism from (0,1) to R instead of checking properties of arctan. Fuckin' idiots with their idiotic advice.

>>4336207
>checking properties of arctan
Do you feel the need to rederive all of math every time you solve a homework problem?

>>4336227
No, you imbecile. But I do feel the need to keep solutions as elegant, transparent and simple as possible. And since proving that my suggested homeomorphism is indeed one is a simple but fruitful exercise for OP, whereas proving the necessary properties of arctan probably impossible for him, you still remain a huge retard.

>>4336227
Besides, you scum of humanity didn't even realize that after having established equality up to homeomorphism with your rocket launcher arctan there is no need for anything else to see homotopy equivalence. Instead you decide refer to a pointless and mysteriously retarded post that's probably confusing path homotopy in Euclidean space with homotopy equivalence of abstract topological spaces.

>>4336207
but then you include 0

>>4336262
personally I think arctan is simple + easier to think about, while that solution is ugly. But whatever, I'm out. Don't pop a pimple while you rage!

Yes, I mad. I mad at people using homotopy theory wrongly since it's my weapon of choice every day. Imagine some retard from Naboo taking Obi-Wan's light saber and going to rave with it. Obi-Wan would surely chop his dick off and then make that fucker eat it. And I feel like mofucking Obi-Wan right now.

>>4336296
NO, YOU SHITFACE, READ THE DEFINITION AGAIN!! READ IT MOTHERFUCKER!!

I wonder if there's a homotopism from 1 to .9 repeated.

OP
>map R to (0,1) (open interval)
>>4336207
>map 1/2 to 0
>seriously hope

>>4336327
IT'S CALLED HOMEO-

Nahson, I ain't trippin' at trolls, just at retards.

>>4336278
Dude, chill the fuck out. Arctan is a fairly standard example for a function mapping the reals to a connected, open subset of the reals. That's all the guy asked for.

<span class="math">\frac{\arctan{x}}{\pi}+\frac{1}{2}[/spoiler] fulfills that purpose.
If you want more elegant, you can go with <span class="math">\frac{1}{e^x+1}[/spoiler]. Your shit is ugly compared to it.

>>4336329
See >>4336319

In case you are too fucking lazy: the map I defined goes from (0,1) to R, it says so right after the eqn block.

>>4336332
You don't see the big picture do you? If OP is asking for a homeomorphism from R to (0,1) on /sci/ it means he is already a shitty mathematician. It also means that he is in first semester analysis and hence his TA won't let him use properties of either trig functions or Euler's number just like that. Instead everything has to be proven at this stage, and he surely won't be able to prove any of the above mentioned necessary properties whereas the map I provided is an even more standard and basic example than any of the other shitty ideas. I get snotty fuckers like you every time I'm TA for some beginners lecture. If you can't prove your statements, you go to hell under my watch.

>>4336361
Actually, OP just asked for a map.
So f(x) = .5 satisfies, and is much simpler to check than any other answer. OP comes in for help with his precalc class and you come in shitting the thread up with "analysis" and "homeomorphisms".

>>4336387
Oh, you're the most helpful of us all! After the first and third posts already providing said map, us then realizing that OP might in fact be looking for a homeomorphism and thus deciding to continue helping for free you come along and present your incredible wisdom! BLOW IT OUT YOU ASS

>>4336409
Man OP is probably long gone. I just decided to come in to antagonize your autism. It obviously worked. Pic related. I bet you'd get pissed that the color is slightly off if I wasn't predicting it now.

>>4336429
I am neither autistic nor do I see any discoloration. What I do see though, ironically, is that I have been the one so far avoiding " "analysis" " whereas that first maggot mentioning arctan was actually the one to introduce analysis into the thread! If anyone thinks that a trigonometric function is somehow more beautiful, elegant or simple than a composition of a rational function and absolute value can lick my salty balls.

>>4336458
autism at its finest

>>4336463
autists don't curse that much.