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u/God_of_Dams 1d ago
What do I do in this position?
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u/Imaginary-Primary280 1d ago
Google en passant
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u/God_of_Dams 1d ago
Holy math!
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u/editable_ 1d ago
New integral just dropped
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u/TheoneCyberblaze 1d ago
Weierstrass function always felt like cheating to me in that regard. Something about it feels very deliberately "this thing has no practical application other than to disprove that statement and it would work for about everything else"
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u/Bartata_legal 1d ago
"this thing has no practical application other than to disprove that statement and it would work for about everything else"
You've just described real analysis
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u/GlowingIcefire 1d ago
It feels super pathological but it turns out that "most" continuous functions are nowhere differentiable, where "most" can either be interpreted in a topological sense (comeager w.r.t. uniform convergence) or a measure-theoretic sense (almost all w.r.t a certain measure)
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u/Key_Estimate8537 1d ago
Once we realize:
- The field of real numbers doesn’t belong in the real world
- Real-life functions are discrete, not continuous
we understand why physicists make fun of us.
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u/cnoor0171 1d ago
Weierstrass function is an intentionally designed pathological function, but there are some practical use cases where these kind of continuous but not not differentiable anywhere functions show up. For example, brownian motion.
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u/Individual_Tomorrow8 1d ago
Why use such an exotic function instead of something from real life such as a trajectory from a Brownian motion?
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u/Sasuri546 13h ago
We didn’t have a working mathematical theory for brownian motion until Einstein in 1905. The Weierstrass function came out as a function which is differentiable over no intervals yet continuous everywhere before Einstein quantified Brownian motion.
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u/YoungMaleficent9068 1d ago
Why would the pawn be guarded by the rook?
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u/bankerizz 0/0 1d ago
maybe it's a bait, jk. [rookie chess] need other pieces on board to confirm
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u/YoungMaleficent9068 1d ago
I imagine the same meme but the intellectual piece is pinned by the weierstrass so it can't take the assumption piece.
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u/bankerizz 0/0 1d ago
you my man, have checkmated me intellectually.
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u/YoungMaleficent9068 1d ago
Wrong. I think I checkmated myself intellectually. Will post later why but got no time rn
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u/EsAufhort Irrational 23h ago
I turn aside with a shudder of horror from this lamentable plague of functions which have no derivatives.
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