TITLE: difference between maximal element and greatest element
QUESTION [51 upvotes]: I know that it's very elementary question but I still don't fully understand difference between maximal element and greatest element. If it's possible, please explain to me this difference with some examples etc.
I tried to explain this difference to myself using only definition, but maximal element and greatest element still seems almost the same for me.
Thank you.

REPLY [12 votes]: Suppose you have a set of boxes. A box that does not fit into any other box is maximal. A box into which any other box fits is greatest.