Why 0.999... Is Not Almost 1

Most classes hand you a slick proof that 0.999... = 1 — and somehow you still don't quite believe it. There's a good reason for that: the famous proofs quietly assume the very thing they're trying to prove. Chapters 0:00 The sliver you can feel 0:40 The proofs you've seen 1:33 Where those proofs cheat 2:21 What 0.999... actually means 2:49 Watch the running total 3:28 Name a gap — any gap 4:10 The honest definition 4:56 "Just infinitely close"? 6:13 There is no last nine 6:59 Zeno, and a little history 7:38 Two names, one point The Long Way makes math videos that skip the shortcut and walk the whole path, so the result is something you can stand on, not just something you were told. Subscribe for more. #math #0999equals1 #infinity #calculus #mathematics