However, the Grassmann numbers can’t have particular real or complex values, not even infinite values, as I will discuss momentarily. Instead, they may be viewed as intrinsically “infinitesimal” in character. That’s why we don’t write the “plus minus infinite” limits on the definite integral.

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The square of a Grassmann variable has to vanish because it’s equal to minus itself and zero is the only number that has this property. The vanishing of the square, θ^2=0, is also satisfied by “infinitesimal numbers” because we neglect (dx)^2 if we only calculate at the accuracy of dx. That’s why the Grassmann numbers are sometimes said to be “infinitesimal”.

— Celebrating Grassmann numbers

— Lubos Motl

2013.08.11 Sunday ACHK