>differentiable everywhere and continuous nowhere>either the concept of differentiable is bullshit>or the density of irrationals in rationals (and vice versa) is bullshit>effectively reals are bullshit Pick your poison.
>>16928918>differentiable everywhereUh, no. It's literally an easy exercise in calc 1 to show that differentiability implies continuity.
It is nowhere differentiable. I am going to be charitable and assume you meant to say it's not Riemann integrable.
>>16928918>differentiable everywhere and continuous nowherethis doesn't even need a proof to disprove because you're just violating a definition
>>16928995That differentiable functions are continuous is a theorem, not a premise.Let [math] \left(\mathbf F,+,\times,\tau_{\bf F}\right) [/math] be a topological field, [math] \left(X,+,\cdot,\tau\right) [/math] be a TVS over it, [math]D[/math] be a subset of [math]\bf F[/math], [math]x[/math] be a point in [math]D[/math] and [math] f:D\longrightarrow X[/math] be have a derivative [math] \delta [/math] at [math]x[/math] (in a non-Hausdorff, derivatives aren't unique).Let [math]W[/math] be a neighborhood of [math]\bf 0[/math]. Choose [math] V\in\mathcal N\left(\mathbf 0\right) [/math] such that [math] V+V\subseteq W [/math]. By boundedness of singletons, there exists [math] U_1\in\mathcal N\left(0\right) [/math] such that [math] U_1\delta \subseteq V[/math]. There also exist [math] U_2 \in \mathcal N\left(0\right) [/math] and [math] U_\delta \in \mathcal N\left(\mathbf 0\right) [/math] such that [math] U_2U_\delta \subseteq V[/math].By differentiability, there exists [math] U_2\in\mathcal N\left(0\right) [/math] such that[eqn] \forall y\in D \cap \left(x + U_2\right), \frac{f\left(y\right) - f\left(x\right)}{y - x}\in \delta + U_\delta.[/eqn]Put [math] U_x=U_1\cap U_2 [/math]. Then for all [math] y \in D \cap \left(x + U_x\right) \setminus\left\{x\right\} [/math],[eqn] f\left(y\right) - f\left(x\right) = \left(y - x\right) \frac{f\left(y\right) - f\left(x\right)}{y - x} \in U_x \left(\delta + U_\delta\right) \subseteq U_x\delta + U_xU_\delta \subseteq U_1\delta + U_2U_\delta \subseteq V+V \subseteq W. [/eqn]And [math] f\left(x\right) \in f\left(x\right) + W[/math]. It follows that [math] \exists U\in\mathcal N\left(x\right), f\left(U\right) \subseteq f\left(x\right) + W [/math]. Since this holds for all such [math]W[/math], we conclude that [math]f[/math] is continuous at [math]x[/math].
>>16929034autism
>>16929034I was thinking of dimensional differentiation. Think of points as circles and then the differential is the tangent to two circles that are closest to one another. Then I started thinking about alternative geometries and spaces and decided I am too retarded to know what I am even doing. So I spend my days vibe coding.
>>16928936>>16928951It's weakly differentiable which is more than enough for anything that matters.
>>16929371it's biblically differentiable.
test
>>16929359ooga booga grug see symbol grug scared
>>16930712you posted some totally irrelevant shit. who the fuck cares about proof in an obvious troll thread? autists, that's who.
>>16930726what if >>16929034 is OP and she's correct and you're just assuming it's a troll thread because of lead poisoning?purely hypothetical, of course, we all know you don't have lead poisoning
>>16930701passed
>>16929034>>16928918so what's the solution here bros?
>>16932646You need a better concept of differentiablity than the one taught in Calculus 1.https://en.wikipedia.org/wiki/Weak_derivative#Examples
>>16932646Solution to what? OP is just a retard who doesn't know his definitions, and there is no paradox.
>>16928918What was your goal when you made this thread? To troll someone or like, piss someone off enough that they would want to engage with this topic out of frustration? And then you bitch and complain when people call you a fucking retard and/or are genuinely confused why the fuck you even made this thread?Do you not know how to initiate ordinary constructive discussions? The fuck is wrong with you?
>>16929034>Let… such that… it follows… we conclude…Everything you wrote is schizo babble
>>16928918Reals are poison
>>16932649you don’t need any of that if you build calculus on formal power series
>>16932708Why does this line of questioning make you so upset?
>>16928918That's an Easy answer: reals are bullshitNext question
Alright /sci/ is this function differentiable?
>>16935847maybe?
>>16930697yes
>>16935847Yes of course it is.
>>16932992If it makes you feel any better I cant read any of it either, only sometimes if the equation is small enough to guestimate.But you wont see me LARPing I knew what meant...
>>16945805Get the fuck out of this thread, schizo. You aren't wanted here. Stick to your containment threads.
>>16945932Whats a "Real" number?
>>16945932>containment threads>>16945937>"Real" numberI rather liked Norman's Dedekind cut take, I did similar things with other "infinities, so I recognized it when I heard it.There is no such thing as "unfamiliar board topic" to me.
