[wenc]

Yes, I came across something like that in my numerical computation course. This was for me the most compelling visualization of what a floating point number was.

The floating number line is actually an (unevenly spaced in reals, uniformly spaced in binary) discrete number line that was used to approximate continuous infinite real numbers, in finite precision e.g.

Reals

0 __________________________________________________ 1

Floats

0 .. .... .. ... .. ... ... ... .. ... ... ... .. .... ... ... ... . ... .... ... .. . ... 1

[saagarjha]

A more accurate representation might be

  0.... . . . .  .  .  .  .    .    .    .    1

(Hacker News eats consecutive spaces, it seems like :/)

[wenc]

Correct about spacing. More accurate reproduction here:

https://www.volkerschatz.com/science/float.html