I am currently studying tensor space theory (over a field) and was reading through the generic Wikipedia article for tensors when I cam across the following:
A type $(p,q)$ tensor $T$ is a multilinear map, $T: \underbrace{V^*\times...\times V^*}_\text{p-copies}\times\underbrace{V\times...\times V}_\text{q-copies} \to K$ where $K$ is the underlying field.
Where the author(s) then goes onto define the notation for the tensor product as
$\underbrace{V\otimes...\otimes V}_\text{p-copies} \otimes \underbrace {V^* \otimes...\otimes V^*}_\text{q-copies}$
My question: why did they flip the usage of the $p$'s and $q$'s? Namely, they first called copies of the dual space $p$ and copies of the vector space $q$ $-$ then went on to reverse this in the notation for the tensor product (calling copies of the vector space $p$ and copies of the dual $q$). Is this an error that should be corrected? I also noticed this in a lecture by Frederic P. Schuller on tensor space theory. He did the exact same thing when defining what a tensor is and then the tensor product (at minute $29:23$).
Please correct me if I am wrong, as I am new to differential geometry and tensors.