I believe I tried to be as specific as possible namely by numbering the questions, showing a solution and then showing my own solution. How do I improve please?
from the comments...
The question was closed as unclear. From what I've read, it appears you start with one question and move on to others, which may be a source of confusion, and possibly the source of other close votes, particularly that asking multiple questions per post is generally frowned upon and usually results in closure as "too broad" (even though they are part of your proof verification). I would suggest reducing the questions and asking something broader, such as "Where did I go wrong?"
You also use images for some sections, even though the relevant content is not very lengthy to type out.
As far as I can tell, the question seems fine, so I'm voting to reopen.
Your question still has a lot of issues in my point of view.
For instance, certainly you don't mean $z=1$ in your first block quote. The notation $C[0,1]$ can also arguably be considered very suboptimal (c.f. What does $C[0,1]$ mean?). Those are minor issues which would be easily fixable through edits, but add up to the existing problems: what the edits have effectively done imho was just to remove the sub-questions explicitly, but those still exist under the guise of "Please point out any errors", where it isn't even explicit anymore where do you think that there are errors.
Note also that there is no actual question in your entire question (interrogation marks are non-existent). What most closely resembles a question is the "Please point out any errors". Note that the answer (which is the accepted one) disregards that altogether, and answers the question in the title (through different means). It isn't clear to me, even after the edits, if you want help through the proof you mention or if it is just you showing your attempt. See this, specifically the "Make your actual question stand out" guideline, for more information on how to improve in that aspect. Also consider tagging for proof-verification if it is indeed the case that you want help through your proof.
So, how to improve the question?
- If you want a proof for the statement, but not necessarily following the proof you mention, then consider shortening the proof you allude to. Show the core aspects, and allude to where you were confused about the validity of some argument, but don't enter a formal, complete proof environment (this is not a rule, but a rule of thumb instead).
- If you want your proof checked, consider tagging the question as such (as I mentioned previously). It can be relatively difficult to make a good question under that objective: as you've seen, if you try to be specific, you can end up asking multiple questions, which is frowned upon. If you are not specific, people can end up thinking it is unclear what you are asking. There are a lot of discussion in meta about those types of questions (c.f. the solution-verification tag here on meta, where you can see a lot of information).
PS: I have not voted to close the question after making the previous considerations. They were made since your question here in meta had the objective of improving the question, not even mentioning the fact that it was closed or not.