Multiplication table for single number

#include <iostream>
#include <string>
#include <cctype> // isdigit()
#include <vector>

using namespace std;

// This function returns true if a string represents a number.
// Otherwise, it returns false.
// 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 your_number = ""; // User input from the console is a string.
    float your_number_float = 0.0; // User input converted to a float (has a decimal point).
    vector<float> table; // This is a list of the values for the multiplication table (input times 1 to 12).

    cout << "\n This program will\n"
        " print a multiplication table\n"
        " of your number from 0 - 12\n\n";

    cout << " Enter a number: ";
    getline(cin, your_number); // Store user input. User input from the console comes in as a string, not a number.

    while (!validate_number(your_number)) // Use validation function to make sure the string input is a number (see above).
    {
        cout << " " << your_number << " is not a number.\n";
        cout << " Please enter a number: ";
        getline(cin, your_number); // Get new user input.
    }
    your_number_float = stof(your_number); // Once you know the string number is valid, convert it to an actual number.

    for (int i = 0; i <= 12; ++i)
        table.push_back(your_number_float * i); // Calculate the number times 1 to 12 and store them as a list.

    // Display the results.
    cout << " \n\n---------------------------------\n"; // Begin title.
    cout << " Number " << your_number_float
        << " multiplied by 0 - 12\n\n"; // End of title.
    cout << " " << your_number_float << " x\n" // Begin top of table.
        " ---------------------"
        << '\n'; // End top of table.
    for (int j = 0; j <= 12; ++j) // Diplay each calculation, 1 to 12.
        cout << " " << j << "  | "
        << table[j] << '\n' // This is the calcualtion stored on the list.
        << " ------------\n";

}