# Understanding the proof of the halting problem [closed]

I came across the following example that proves that the blank tape halting problem is not decidable.

I understand the proof technique, but I just don't see how the blank tape problem is shown to be undecidable in the proof.

It says $M_{w}$ starts with a blank tape but then writes $w$ onto the tape, so there is no difference to the general halting problem.

How does this imply that the blank tape halting problem is not decidable? I can't find the logical conclusion. Couldn't we just replace the blank tape halting problem with another DECIDABLE problem and argue the same way?

• Please don't use images as main content of your post. This makes your question impossible to search and inaccessible to the visually impaired; we don't like that. Please transcribe text and mathematics (note that you can use LaTeX) and don't forget to give proper attribution to your sources! – D.W. Nov 25 '15 at 18:54
• Won't happen again. – Javiator Nov 25 '15 at 18:57
• Please edit it away now. – Raphael Nov 25 '15 at 19:16
• "I understand the proof technique, but I just don't see how [...] is shown [...] in the proof." -- This sentence seems self-contradictory to me. Note that this is a proof sketch. Flesh out the details to see clearer. – Raphael Nov 25 '15 at 19:18
• This seems more a logic issue than a computer science one. If A implies B and B is false than you can deduce that A is false. A can be true only if B is also true does not mean that if B is true you can deduce that A is true. (A is "the blank tape problem is decidable", B is "the halting problem is decidable"). – AProgrammer Nov 26 '15 at 10:48