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7:53 AM
@Mathphile Hi , at the moment I try to factor 10^100 + 9^9 with pari. Do you know how to recover chatjax ? I had an issue with windows and now use ubuntu.
 
 
9 hours later…
5:09 PM
@TheSimpliFire any idea if this is abuse of the conjecture tag?
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Q: Integral form of work during an irreversible process?

More AnonymousQuestion Why can't the work during an irreversible process be integrated? Where is my understanding amiss? Motivation (for this question) A lot of my physics background seems to say this is a math problem. My understanding of the problem can be summarised by: -lecture slide where $P$ is pr...

 
 
3 hours later…
8:29 PM
Likely of interest to no-one, but I made ordinal hyperoperators:
$$\alpha\uparrow^\mu\beta=\begin{cases}\alpha\cdot\beta,&\mu=0\\1,&\mu>0\land\beta=0\\\displaystyle\sup_{\mu'<\mu\\\beta'<\beta}\max\{\alpha\uparrow^{\mu'}\alpha\uparrow^\mu\beta',\alpha\uparrow^\mu\beta'\uparrow^{\mu'}\alpha\},&\text{else}\end{cases}$$
They have lots of nice properties, namely a nice base-changing formula:$$\alpha\uparrow^\mu(\beta+\gamma)=(\alpha\uparrow^\mu\beta)\uparrow^\mu\gamma$$for limit ordinals $\beta,\gamma$ and $\mu\ge2$.
 

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