the characteristic number of infinite field is
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Answer:the rational functions in the indeterminate T with coefficients in Fp (the symbol Fp is just a synonym for Z/pZ). In other words, these are ratios of polynomials in Fp[T]; this is the same construction as the one we use to make Q from Z. The field Fp(T) is infinite because, for example, it contains 1, T, T2, …, and it is of characteristic p because it contains Fp (alternatively, because the kernel of the unique ring homomorphism Z→Fp(T) is pZ.)
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