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from wikipedia: "Suppose an enveloping manifold M has n dimensions; then any submanifold of M of n − 1 dimensions is a hypersurface"

Now, hyper- is the prefix of "over" hypo- is the prefix of "under"

If we move form n to n-1 soundn't it be called Hyposurface?

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I believe the "hyper" prefix is used since hypersurfaces are the higher-dimensional analogs of regular two-dimensional surfaces? – Vhailor May 3 '11 at 11:46
    
@Vhailor- Publish your comment as a question and I will select it – idober May 3 '11 at 12:12
up vote 3 down vote accepted

The "hyper" prefix is used since hypersurfaces are the higher-dimensional analogs of regular two-dimensional surfaces.

It is used in the same way in expressions such as "hyperplane" and "hypercube".

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