Comment Tess Rinearson's original post... (Score 1) 353
Tess Rinearson's blog post (referenced by Philip Guo) at https://medium.com/tales-from-the-front/cc9ed433ec3c is as strong as Philip's - well worth reading.
Every nonzero finite dimensional inner product space has an orthonormal basis. It makes sense, when you don't think about it.