I caution against looking at numbers in any single way. The more different ways you can visualize math concepts, the better. Practice seeing them in different ways.

Sometimes numbers are for quantifying a pile of things, and 255 and 256 are basically the same.

Sometimes numbers are for cryptographically signing things, and 255 is extremely secure while 256 is completely vulnerable.

Sometimes numbers are for arranging tournaments, and 256 is a tremendously useful number while 255 is super annoying and you should look for another.

Sometimes numbers are stored in a single byte, and 256 (=0) is the friendliest number you will ever know, while 255's words are BACKED BY NUCLEAR WEAPONS.

Sometimes infinity is a useful number, sometimes it's not. Sometimes 1/2 is a useful number (pies), sometimes it's not (babies). Sometimes sqrt(-1) is a useful number, sometimes it's not. Sometimes the sum of all positive integers equals -1/12; sometimes that's stupid.

All of these situations may call for visualizing numbers differently.