The way I like to explain it to get it to quickly click in anyone's head (math geek and non-math geek alike) is so: What is true about any two distinct numbers

The way I like to explain it to get it to quickly click in anyone's head (math geek and non-math geek alike) is so: What is true about any two distinct numbers? Answer: there are an infinite number of numbers between them (e.g. between 4.00005 and 4.00006 there are 4.000051, 4.0000501, 4.00005001, etc. You can always add more zeros). But one cannot name a single number between 0.9999... and 1 because they are the same number. Not really an actual, rigorous proof, but it serves its purpose.