Ambiguity, IntenSion and Relevancy

An Infinite Set of Attributes?

How many attributes does the string “(31 - 7.5) * (2 + 4)” have? Or, which is equivalent, in how many ways can that string be described? I argue that the number of ways I can describe the string “(31 - 7.5) * (2 + 4)” is infinite. Yes, infinite. Here are some attributes I can use to describe that string:

the number of multiplication (‘*’) operators
the number of odd numbers
the number of integers
the number of operands
the number of operators
the number of parentheses
the number of spaces
the length with spaces
the length without spaces
the number of spaces after an odd number
…
the number of three decimal points
…
the number of 1 digit integers
the number of 2 digit integers
the number of 3 digit integers
the number of 4 digit integers
…
the number of 3’s in the string
the number of 4’s in the string
the number of 9’s in the string
…
etc.