Talk:Axiom of Choice implies Zorn's Lemma/Proof 2

Meaning of square brackets

What is the meaning of the square brackets in

\(\ds \map h \lambda\)

\(=\)

\(\ds \map f {\map g {f \sqbrk \lambda} }\)

if $\lambda$ is a limit ordinal.

Is it something to do with ordinals? Is it the application of a function to a set (i.e. $f \sqbrk X := \set {\map f x : x \in X}$)? Whatever it is, it should be explained in the proof.

I've taken a look. Not one of my pages this one, so I'm not sure myself. But there is a fair amount of specialised notation in the exposition of ordinals (which was going to be reviewed and rationalised at one point, never got round to it) where it may be explained. I've added a maintenance tag to it with a view to revisiting it. I've also taken the opportunity of tidying up the source code while I was about it. --prime mover (talk) 12:07, 19 April 2019 (EDT)

The line "when $h \sqbrk \lambda$ is the image set of $\lambda$ under $h$." can explain it. Leonhard Euler (talk) 20:38, 26 June 2021 (UTC)

Not really. You've got $\map h \lambda$ on one side of the equation, which is the thing you're trying to define, and you've got $h \sqbrk \lambda$ on the other, which is what you're trying to define $\map h \lambda$ in the first place. On the surface that makes it a circular definition.

If you really know your way around this area, you are welcome to offer citations to where this construct can be found. Admittedly the person who originally posted this "proof" up didn't well explain what he put, and it is highly likely that there *is* no source work with this in. But in his original, there was no circularity of quite the kind I see here. --prime mover (talk) 20:52, 26 June 2021 (UTC)

Oh, and by the way, please sign your posts. --prime mover (talk) 20:53, 26 June 2021 (UTC)

I didn't understand what's the problem with the definition. We defined $\map h{\lambda}=\map f{\map g{\{h(x):x\in\lambda\}}}$. The definition is by transfinite induction. --Leonhard Euler (talk) 21:19, 26 June 2021 (UTC)

So you're good at repeating yourself at a higher volume, but not explaining, then? Wotever, you do you. --prime mover (talk) 21:30, 26 June 2021 (UTC)