>>10148228I didn't understand what you were trying to ask. Were you simply asking whether your definition of an arbitrarily large number was well defined? If so, then NO, YOUR DEFINITION WAS NOT WELL DEFINED.
The main problem is that you're trying to DEFINE . So, when you WANT TO DEFINE SOMETHING, YOU CAN'T CLAIM IT'S DEFINITION IS CONDITIONAL.
Your definition breaks down exactly at this point
.
The definition of is conditional on the you choose from and hence you may not have the same every time with your definition.
