That's not a definition. Neither 10^∞ nor 1/∞ is defined in any standard system, so you'll have to define those too if you want to use them to define 0.000…1.

See https://en.wikipedia.org/wiki/Surreal_number .

You're working with surreal numbers? This is not what people would expect unless it's explicitly stated. In addition, you're likely going to have a hard time explaining surreal numbers to someone who struggles to grasp that 0.999... = 1 in the ordinary reals.

Surreal numbers and infinistemal are simpler to work with when you need to work with infinite series.

Here John Conway explains them: https://www.youtube.com/watch?v=1eAmxgINXrE