[falserum]

Is 1/10 (also known as 0.1) a valid number in base 10?

What about same number expressed in base 3? (I think in base 3 that would be written as 1/31)

And what about number 0.1 in base 3? (Which is equivalent to 1/3 in base 10)

[ludston]

You can have as many different symbols as you like, so long as you can actually write them on paper. As soon as you tell me that one of those symbols is a number with infinite digits I will disagree with you, given that you are unable to tell me what those digits are before the universe ends.

[AnimalMuppet]

I can tell you that the number is 0.1 in base 3, which defines the number precisely. Or I can tell you that it in base 10, it has an infinite representation, and all the digits are 3. There, I told you what they all are, and the universe has not ended yet.