There are insane positions in infinite chess, a kind of chess warfare, involving a bishop gun battery, where black can fire arbitrarily large bishop guns; each bishop moving out is a kind of bullet, and white must answer at every step. But white ultimately wins, even though black, "doomed", has these various harassment possibilities.

I think it is just the usual order on the rational numbers, but since he uses only some of the rationals, it does amount to using ordinals.

But, I think your solution is off by at least a factor of omega.

I see, he has limit ordinals in his embedded order with the sequence 1 - (1/2)^n, with 1 being the equivalent of omega.

You probably even could get an embedded omega squared with

1 - (1/2)^n - (1/3)^m with m>n

So 1/2 = omega

3/4 = 2 * omega

7/8 = 3 * omega

and 1 is omega * omega

He might have omega squared in his version, but I didn't read it that carefully.

Now play the version where the secret ordinal is an uncountable ordinal or a strongly inaccessible cardinal.

Wow, what a nice testimonial!

The V-E+R follows the pattern of zero-dimensional, one-dimensional, two-dimensional, and this alternating sum formulation continues for the Euler characteristic in higher dimensions. So that is one reason to keep V-E+R.

Another reason, however, is that although some negative numbers show up, the numbers are all very small, and this could be a good opportunity to introduce some exposure to negative numbers.

Screenshot of the site: http://i.imgur.com/yFfyjN0.png