I have a degree in math, I know about Lesbegue measure and probability. My math knowledge is slightly more sophisticated than you give me credit for, if not muc

I have a degree in math, I know about Lesbegue measure and probability. My math knowledge is slightly more sophisticated than you give me credit for, if not much more! What you're describing is, to me, the "slippery way" that there is always one more. Yes, one more than a countable set implies infinitely many more, clearly, because there will always be one more even after adding another (or a countable number.) However... the point I'm attempting to articulate - which is not defined precisely and hence is not mathematical, is that almost all just doesn't work in my brain if there are an infinity of "countable" numbers between any two "uncountable" ones!