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Barnett's infinity is the largest known infinity. A set is said to be "Barnett Infinite" if there exists a bijection between the set and the set of Barnett integrable functions [math]\mathcal{B}[/math]
[math]\mathcal{B}=\left \{f \in C(\mathbb{R})~:~\int \int \int f(x)~{\mathrm{d}^3 x}\leq \frac{-e^{i\pi}}{11.999...}\right\}[/math]
An interesting theorem is that a Barnett infinite set is infinitely more infinite than any countable set (Barnett, 2012).
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>>8312908
[math]\mathcal B \subseteq C(\mathbb R)[/math] so [math]|\mathcal B| \le |C(\mathbb R)| = \bigl| \mathbb R^{\mathbb Q} \bigr| = \mathfrak c^{\aleph_0} = \mathfrak c < \mathfrak c^+[/math]
go meme somewhere else
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>>8312908
But every student knows there is precisely one unique Barnett-integrable function to within isomorphism familia
Check your proof
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>>8313070
>perfectly good thread
>page 10
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>>8312908
>An interesting theorem is that a Barnett infinite set is infinitely more infinite than any countable set (Barnett, 2012).
I kek'd
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>>8312908
das a lot of integrals mang
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>>8312908
> read this
> feel like a brainlet
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>>8312908
The barnett integrable space truly is wondrous. At the head of mathematics, even pulling forward beyond inter-universal techmuller theory, this infinity takes the complex subject of triple integrals to a place beyond the imagination of the unenlightened. Even I, a great achiever with a phd in triple integrals, cannot begin to grasp the significance of such wondrous occurences as euler's identity, the evaluation of .9999..., and the sum of all natural numbers within barnett's magnum opus. How can math be so amazingly connected? How can it be so pure, so beautiful?
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>>8312908
>Barnett's infinity is the largest known infinity.
Why not just take the power set of a Barnett infinite set?
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>infinite sets
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>>8312908
Xinfinity <- is the largest infinity, I don't know what it is exactly, but that word represents the largest infiinity there is in all models.
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