Is there a normed space which is isometric to a proper subspace of itself?

[mathmaniac]

My understanding is that there is such a normed space due to coming across https://math.stackexchange.com/questions/1738410/normed-space-isometric-to-proper-subspace-of-itself, however I don't understand the explanation, if that even is an explanation at all in the comments. Could someone please explain or help? Thank you.