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Extending the hyperoperators to all real or complex values is a known open problem. Some time ago I had a somewhat converse idea on how to approach this  instead of starting with a fast growing function(s) on natural numbers and extending it to more inputs, we can directly construct a sequence of fast growing functions defined for all complex values. I do not claim this is of as much interest as extending hyperoperators, but might nevertheless be interesting for some.
Suppose we have chosen a system of fundamental sequences for countable limit ordinals up to some bound. We now construct a sequence \(f_\alpha:\mathbb C\rightarrow\mathbb C\) which satisfies the following propertes:
 \(f_\alpha\) is an ,
 \(f_\alpha(z)\in(0,\infty)\) for \(z\in\mâ€¦

Because of Emlightened's recent blog post I was pushed to think again about FOOT, truth predicates and related. The conclusion I came to is:
 FOOT is not as strong as I thought it is. Indeed, it is about as strong as FOST with a single truth predicate added. However, it still seems that at the time of definition BIG FOOT was the largest number explicitly defined (in particular, larger than Fish number 7), and possibly still is.
I will address the three parts separately below.
When defining FOOT, I first defined \(\text{Ord}\), on order to be able to define the truth predicate with help of it to be able to define Rayo's function. As Emlightened points out, we can't get the full truth predicate this way  we only get it for formulas with parametâ€¦
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If I'm online, mention me (write "Wojowu" in the chat). Once I answer, you know I'm active.
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Hello everyone. Today I am bringing you a public service announcement regarding our IRC channel.
Over a past few months we've had many new users join our wiki, and our IRC channel isn't really welladvertised anywhere. Because of that, I wanted to semiofficially invite all of you to join us there! You can find all the instructions written up here. Let me also remark that the chat at many times is rather inactive, but if you see me (Wojowu) online, feel free to highlight me so I know someone is around!
See you all there!
(btw, if you want to be noticed, I recommend staying there for more than 85 seconds (I am looking at you, Mush9))
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Recently a BMS artist called LeaF has released a song called â„µ0 (Aleph0). I thought some of you might be interested by this because of the cardinal number reference in the title.
You can check out the song at the composer's SoundCloud, or on Youtube, accompanied with the official video (which I personally very much like). You can also check out the BMS chart of this song, if you want.
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