When does a double become NaN?

I am trying to understand which circumstances can cause a double to become NaN.

For instance, 0/0 is nan. This is also stated in the official Documentation. https://docs.microsoft.com/en-us/dotnet/api/system.double.nan?view=net-6.0

However, my debug code indicates that the division is not by 0:

public class StandardDeviation
{
    public StandardDeviation()
    {
        Clear();
    }
    private double M { get; set; }
    private double S { get; set; }
    private uint Iteration { get; set; }
    public double Value
    {
        get
        {
            return Math.Sqrt(S / (Iteration - 2));
        }

    }
    public void AddValue(double value)
    {
        if (double.IsNaN(value))
        {
            throw new ArgumentException("value IS nan!");
        }
        double tmpM = M;
        M += (value - tmpM) / Iteration;
        S += (value - tmpM) * (value - M);
        Iteration++;
        if (double.IsNaN(M))
        {
            Console.WriteLine($"\nNAN EXCEPTION!!! divide by: {Iteration}");
Console.WriteLine($"\nNAN EXCEPTION!!! tmpM: {tmpM}");
            throw new ArgumentException("m IS nan!");
        }
    }
    public void Clear()
    {
        M = 0.0;
        S = 0.0;
        Iteration = 1;
    }
}

console message:

NAN EXCEPTION!!! divide by: 3
NAN EXCEPTION!!! tmpM: ∞

The issue primairly seems to be prevalent in release configuration, which makes it hard to debug.

Whenever the exception is thrown, Iteration = 3.