I have been astonished at the response to publicity surrounding my research. A great many of you have commented on one example of transreal arithmetic that I used in the TV package. I have replied to many of you individually, but I regret that I do not have time to reply to you all. Debate will be improved if you read my papers. The first paper describes the arithmetic in terms of operations on fractions. It predates the axioms paper. http://www.bookofparagon.com/Mathematics/PerspexMachineVII.pdf The second paper gives the axioms: http://www.bookofparagon.com/Mathematics/PerspexMachineVIII.pdf The third paper gives a development of the exponential, logarithmic, and trigonometric functions. There is an error in the guarding clause of equation 10, but this does not affect anything else in the paper. Nor does it affect the demonstration I gave in the TV package. http://www.bookofparagon.com/Mathematics/PerspexMachineIX.pdf Here is another proof of the 0^0 result. It is justified in the analysis paper. 0^0 = e^(ln 0^0) = e^(0 x ln 0) = e^( 0 x (-infinity)) = e^nullity = nullity James Anderson, Univesity of Reading [via Guy Haworth]