I will translate and write a perfect article in Thai for you 500 words for $10

I will translate and write a perfect article in Thai for you 500 words

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co.combinatorics – Is there a prefix-continuous bijection between finite words and eventually zero words?

Let
$$ X = {x in {0,1}^{omega} ;|; exists m: forall i geq m: x_i = 0} $$
(one-way infinite eventually zero words). Let ${0,1}^*$ denote the finite (not necessarily nonempty) words over ${0,1}$, and write ${0,1}^{leq k} = {w in {0,1}^* ;|; |w| leq k}$ where $|w|$ denotes length.

Is there a bijection $phi : X to {0,1}^*$ such that
$$ exists n in mathbb{N}: forall a, b in {0,1}^{leq 1}: forall x in {0,1}^{mathbb{N}}: exists c, d in {0,1}^{leq n}: exists y in {0,1}^*: phi(a cdot x) = c cdot y wedge phi(b cdot x) = d cdot y $$
holds, where $cdot$ is concatenation?

This is a kind of continuity assumption, and seems vaguely familiar to me but I don’t know from where, and I’m not seeing how to construct $phi$. The straightforward idea of cutting out the zero tail doesn’t work because it’s not surjective, and I run into trouble trying to fix that. But I also didn’t manage to prove impossibility because there’s a lot of freedom.

The question arises in some (leisurely) research, so asking here instead of math.SE even if it might be safer to start there with this one. Geometric group theory tag because this is related to Thompson’s $V$, even if I didn’t elaborate and I doubt it’s useful (every countable group acts freely on ${0,1}^*$).

usability – Convey the meaning of any without using words

There is a design with several dropdowns to select between multiple choices.

This choices work as filters on a large dataset, when you select one of them only the records matching the selection will be displayed.

The first choice is always “all”, meaning that you don’t care about that particular category.

The problem is that when translated, for languages that have genre, the translation is different depending on the genre of the category, and it’s difficult for the translation engine to provide an accurate translation.

So, we want to convey this meaning using a language independent simbology. Right now we have a combination of lines and a star:

screenshot

But I am not sure this design is the best one to convey the meaning.

What could be the best alternative? (Any Unicode symbol can be used)

But

Word 2016 breaks words with superscript symbols from the “phonetic extensions” unicode block

I’m using superscript letters from the “phonetic extensions” unicode block (U+1d2c through U+1d61) in scholarly transliteration in a Word 2016 document. Unfortunately, Word keeps treating these symbols as if they were punctuation, breaking the word and completely defeating the purpose of that segment of the unicode. It does not do this with other non-superscript parts of that unicode block nor with superscript symbols from other blocks (such as anything from the “Superscripts and Subscripts” block or U+02B0 through U+02C1 of the “Spacing Modifier Letters” block).

For instance, the word ˀĒͅyᵊṯānᵊ is treated as if it is two words ˀĒͅy and ṯān and the two symbols function as if they were punctuation. It’s as if I wrote the word as ˀĒͅy,ṯān, (with commas instead of ). I cannot select the whole word through double clicking it nor will it be treated as a single word in spellcheck.

How do I fix this? This has been a massive waste of my time, as I cannot spellcheck academic documents (even if I add words to the dictionary) unless I go through them by hand.

Thanks!

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