According to Wikipedia,
Hilbert space [...] extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions
However, the article on Euclidean space states already refers to
the n-dimensional Euclidean space.
This would imply that Hilbert space and Euclidean space are synonymous, which seems silly.
What exactly is the difference between Hilbert space and Euclidean space? What would be an example of a non-Euclidean Hilbert space?