isn't it just the finite field represented by the set of symbols and places?
Discussion
No. You can easily define numbers larger than the set. Which means the largest number you can describe with words is somewhere within the set.
you can only define numbers larger than the set if you allow the set to be expanded in some way. more symbols, more places.
The symbols only have meaning if you give them meaning. Let's say I give you five places 0-9 and the lower case alphabet. So you write 'zzzzz' as the largest integer therefore '100000' must be the smallest integer that can't be defined right? Well I'd argue that 'zzzzz' doesn't define anything since it doesn't define its own base. What if you had written 'tree3'? Is that a base 36 or the usual huge number we normally define it as?