Joining 2 Paths in Adobe Illustrator

Question

I am not 100% sure how to word this question being new (very novice getting to grips with the terms) to Adobe Illustrator so going to give it a shot - it might be a duplicate - as I don't know exactly what I am searching for. Please be gentle.

I have traced an object (hard hat) and I have ended up with 2 paths.

This consists of the outer shell of the hat, and the inner top part of the hat.

The additional curve sticking out was to join some paths. This needs to go.

Question(s)

How can I join the two paths and remove that outer curve to tidy this up?

Zooming in closely to the outer curve, you can see the anchor points from the 2 paths are close.

Can you join these anchor points from two different paths manually?

What I have tried

I have tried countless options from Path finder - but I just want to tidy the lines. My google efforts:

adobe illustrator merge anchor points different path
adobe illustrator merge anchor points
adobe illustrator combine shapes

Answer 1

What your asking directly can not be done because that would result in a nonmanifold geometry. While nonmanifold geometry would be useful to you its of no use for the drawing of the data. Illustrator is a direct modeler (for most part) so its your job to directly do the drawing instructions.

So never can you have three or more curves coming from a point, btw illustrator calls points vertices (plural for vertex). That does not mean you can not have two separate vertices on top of eachother. So saying that you merge vetrices from two different paths only makes sense if

1. Both paths are open.
2. Both vertices are the last or first vetex of a path.

In this case you have neither. To underline the point illustrator calls this joining, not merging, because merging vertices makes little sense.

So just move the other point on top of the other point then with direct selection tool .Then select spans that form the bump and hit delete. If you need more complex fill area construction then use shape builder.

Also it might be good to know that using illustrator resembles cutting pieces of paper more than drawing. Do not try to cut exact negbouring pieces out of eachother. Layer them on top. Why? Most vector engines make a assumption that coverage = transparency this is a bad assumption. So try to overlap filled areas unless you want background color bleeding through.