How do I describe a set of names?

Question

I want to describe the following set...

{ "Person1", "Person2", "Person3"... }

... where the number is from 1.. 100.

How do I do this using mathematical set description?

Answer 1

My solution: $$\{\text{"Person"} + \operatorname{str}(k) : 1 \le k \le 100 \land k \in \mathbb N\}$$

whereby $+$ is the concatenation of strings and $\operatorname{str}(\cdot)$ is a function converting a number into its decimal string representation. strings can be mathematically described as finite lists of characters (which is also done in many programming languages).

The advantage: The above statement can be tranfered to many programming languages. For example in python you can write:

set([ "Person" + str(k+1) for k in range(0,100) ])

Answer 2

You can say this: We have $26$ symbols of the english alphabet and $10$ symbols $\{0,1,...,9\}$ that can produce all the numbers. Now your set can be described as $S=\{xn:x=Person$ and $n\in [1,100]\}\subset \mathbb F_{36}$ the free group with $36$ generators.

Answer 3

That set is not a mathematical object. As far as I know, math has not a standard notation to describe such thing. Computer languages or pseudocode may work better for that.