#Euler Measure ?? Homotopy cardinality ?? # of finite sets = e

21 messages · Page 1 of 1 (latest)

harsh widget
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https://arxiv.org/abs/math/0203289
https://arxiv.org/abs/math/0204009

@fresh stratus
Think about why there are only e finite sets. Thats basically the same idea.

So turns out your batsh!t crazy idea for having a non integer cartesian product may not be completely absurd. Theres definitely a lot of leg ~~room ~~ WORK (not in a plane lmao) to be done but it could be a interesting project to construct it using these tools. The actual hard big brain work is mostly already been done which is extending cardinality.

Seems you can equate it similarly to the notion of groupoid/homotopy cardinality (but dont quote me on that mf stupid ass ho dumbass bih ass no dad having mf I just saw a baez post about it i dont understand wtf cohomology finitude even means).

arXiv.org
Euler measure as generalized cardinality

Schanuel has pointed out that there are mathematically interesting categories
whose relationship to the ring of integers is analogous to the relationship
between the category of finite sets and the semi-ring of non-negative integers.
Such categories are inherently geometrical or topological, in that the mapping
to the ring of integers is a varia...

arXiv.org
Exponentiation and Euler measure

Two of the pillars of combinatorics are the notion of choosing an arbitrary
subset of a set with $n$ elements (which can be done in $2^n$ ways), and the
notion of choosing a $k$-element subset of a set with $n$ elements (which can
be done in $n \choose k$ ways). In this article I sketch the beginnings of a
theory that would import these notions ...

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Ratchet ass ho see this @fresh stratus @fresh stratus @fresh stratus @fresh stratus @fresh stratus

fresh stratus
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Wow. This shit is sure interesting.

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This is genius, I would have never thought of this

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okay maybe it is actually really obvious

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This is the most BS technically correct nonsense ever

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im not used to thinking of functions as geometric objects this makes my brain hurt

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he loses me here

pallid rain
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about what, the abel summation? Its one of those silly analytic number theory things that just kinda pops out an answer you like

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im reading the paper and I can accept that the space of piecewise constant functions has a euler characteristic of 1/2 cause I kinda also assume its haussdorf dimension is somewhere around there

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cause the haussdorf dimension of a random process's zeros is 1/2 and you can kinda model the limit of P_n as the space of a locally constant random process

fresh stratus
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I mean, I guess the result is rather nice so I am continuing.

swift remnant
fresh stratus
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He bullied me for my brilliance and now he sees it

swift remnant
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ah

harsh widget
harsh widget