Representing a number and instantiating it are distinct: finite symbols can denote infinite numbers only if an infinite medium (time, space, or computation) is available for arbitrarily long strings.

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Denote(as describing what each character in a notation must do): To directly refer to or stand for something; it's what a word or symbol does when it points to what it means.
Finite symbols(as used in philosophy of mathematics and logic): Limited, countable marks or signs—like individual written digits (0, 1, 2, etc.) that are each just one thing, not infinite in size.
Instantiating(as used in logic and philosophy of mathematics): Actually creating or making real a specific example of something—like writing down the number 5 on a piece of paper is instantiating the abstract concept of five.
Medium(as used in metaphysics and philosophy of mind): The material or substance through which something happens or exists—like paper is the medium you write on, or air is the medium sound travels through.

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