Talk:Triangle Inequality/Real Numbers/General Result

Here are the things I tried to fix:

• Reference to complex cases for the theorem, when this is a real number-specific page
• Reference to "Basis for the Induction" in the induction step, which doesn't really make sense (I think it's supposed to reference the logic behind the basis, but let's just do that directly)
• Separate handling for $\map P 2$, when it can be derived from $\map P 1$ in exactly the same manner as (say) $\map P 3$ is derived from $\map P 2$, etc.
• What appears to be a typo - two lines of the equation are identical. I believe the first of the two is supposed to be:

$\ds \size {\sum_{i = 0}^k x_i} + \size {x_{k + 1}}$

which would mostly make sense in context (number 2 kind of throws it off).

The third of those (separate handling for $\map P 2$) is technically fine to leave, it just kind of defeats the purpose of a proof by induction. I get that it emphasizes that the $n = 2$ case is the same as Triangle Inequality for Real Numbers, but I don't think it's necessary.

I believe at least some parts of my edit can, and should, be incorporated. As it currently stands, the proof is technically incorrect (mostly due to issue 4). --CircuitCraft (talk) 00:20, 13 July 2023 (UTC)

Yes I missed 4, that was the mistake. Having put the modulus around the entire summation instead of the term was an oversight which now I realise I made. Missed it in your edit because there was too much other stuff going on. It's correct now. --prime mover (talk) 05:11, 13 July 2023 (UTC)

The main reason for reverting your changes is because of the link to the induction hypothesis. Seeing that wrong, I reversed the whole thing out to look at it properly this morning after sleep. --prime mover (talk) 05:14, 13 July 2023 (UTC)