Interesting problem (1 Viewer)

[seanieg89]

Here is an interesting problem. If you are not comfortable with higher dimensional spaces, replace "affine hyperplane" with "line" (not necessarily through the origin), and fix n=2 in the below.


Suppose we have finitely many affine hyperplanes
and suppose a point is chosen arbitrarily.

Prove that any sequence defined by:




is bounded, where denotes orthogonal projection onto and the sequence in is chosen arbitrarily.

Is your bound independent of your choice of sequence ?