The explanation I've seen is that ... is notation for something that can be otherwise represented as sums of infinite series.

In the case of 0.999..., it can be shown to converge toward 1 with the convergence rule for geometric series.

If |r| < 1, then:

ar + ar² + ar³ + ... = ar / (1 - r)

Thus:

0.999... = 9(1/10) + 9(1/10)² + 9(1/10)³ + ...

= 9(1/10) / (1 - 1/10)

= (9/10) / (9/10)

= 1

Just for fun, let's try 0.424242...

0.424242... = 42(1/100) + 42(1/100)² + 42(1/100)³

= 42(1/100) / (1 - 1/100)

= (42/100) / (99/100)

= 42/99

= 0.424242...

So there you go, nothing gained from that other than seeing that 0.999... is distinct from other known patterns of repeating numbers after the decimal point.