Is a complete binary tree classified as a forest?

According to Wikipedia, tree and forest definitions are as follows:

Tree: Connected, non-closed, undirected graph
Forest: Undirected Graph with No Closed Paths

The special shape of the forest is trees, so all trees are forests.A complete binary tree is of course a forest.

Here are a few examples: x is a clause and - and | is a branch.

 x --- x
    |
x--- x--- x
    |
    x--- x

This is a tree and also a forest.

 x --- x
    |   |
x--- x--- x
    |
    x--- x

This is not a tree or a forest because it has a closed path.

 x --- x x
    |             |
x---x---x---x---x
    |                
    x--- x

This is not a tree but a forest because it is not concatenated.
(If you look at the two connected graphs individually, they are Tree/Forest)

 x --- x x
    |   |         |
x---x---x---x---x
    |                
    x--- x

This is not a tree or a forest because it has closed paths and is not connected.
(If you look at the graph on the right, it's Tree/Forest)

 x --- x x
    |            |
x---x---x---x---x----x
    |                
    x--- x

This is a tree and also a forest.