Inifinite loop problem (easy question)

[Ulnarian]

Hey all, sorry for all the beginner's questions

Anyways, I'm trying to build a simple loop that will protect against unwanted input (i.e. when the user enters a characters instead of an integer). Here's what I have so far:

#include <iostream>
#include <cctype>

using namespace std;

int main()
{
    
    cout << "Enter a number: ";
    int number;
    cin >> number;
  
    
    while (!isdigit(number))        //Created an infinite loop!
    {cout << endl << "That is not a number, please try again: ";
     cin >> number;}
    
    cout << endl << "Enter a character: ";
    char ch;
    cin >> ch;
    
    cout << endl << number << " " << ch;
    
    int wait;
    cin >> wait;
    return 0;
}

First of all, am I correct that (!isdigit(number)) is really saying "Do this while the input is not an integer?"

Whenever I input a numeric value, say 3, I get the message stating "That is not a number, please try again"??!

Whenever I input a character value, I get an infinite loop stating" "That is not a number, please try again", and the program ignores the cin >> number within the loop.

Can anyone tell me whats wrong here?

Thanks.