Determine if a string represents a number

#include <iostream>
#include <string>
#include <cctype>

using namespace std;

// Determine if a string represents a number.
// There can be one decimal point. There can be a plus or minus sign, if followed by a digit.
// All characters other than . + - must be a digit.
bool validate_number(string number)
{
    int num_decimal_points = 0; // Count decimal points. There can only be one.
    for (size_t i = 0; i < number.length(); ++i) // Check each character.
    {
        if (number[i] == '.') // If it's a decimal point,
        {
            ++num_decimal_points; // Count it.
        }
        else if ( (number[i] == '+') || (number[i] == '-') ) // If it's + or -
        {
            if (!isdigit(number[i + 1])) // If the next character is not a digit,
            {
                return false; // This number is invalid.
            }
        }
        else if ( !isdigit(number[i]) ) // Else if it's not a digit,
        {
            return false; // This number is invalid.
        }
    }
    if (num_decimal_points > 1) // If there's more than one decimal point,
    {
        return false; // This number is invalid.
    }
    // If there's a decimal point but no digits,
    if ((num_decimal_points == 1) && (number.length() == 1))
    {
        return false; // This number is invalid.
    }

    return true; // The number is valid.
}

int main()
{
    string number; // A string that may represent a number.

    cout << "Enter a number:\n";
    cin >> number; // Get the string.

     // If the string represents a number,
    if (validate_number(number))
    {
        cout << "It's a number.\n";
    }
    else // If the string doesn't represent a number,
    {
        cout << "It's not a valid number.\n";
    }
}