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It was presumably proven when it was discovered that there were infinitely many counting numbers. However, whoever it was, did not consider the mathematical possibility with practicality.
The universe has a finite life. Within that our solar system is finite. People, in their turn, have finite lives. In a finite life you can only "dial" a finite number of digits. therefore, you can only call a number if it has a finite number of digits. For any finite number of digits, there are only a finite amount of phone numbers.
So, having infinitely many telephone numbers is no use if you need to wait an infinite amount of time (longer than you'll live) for the first person to call you!
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