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He didn't avoid fractional exponents; only negative exponents don't appear in his work.
Keep in mind that raising a base to a fractional exponent, n, is the same as taking the n th root of that number.
Where n and k _ 0 are a nonzero natural number and an integer respectively ( which are part of the datum of " f " ) : in other words, Puiseux series differ from formal Laurent series in that they allow for fractional exponents of the indeterminate as long as these fractional exponents have bounded denominator ( here " n " ), and just as Laurent series, Puiseux series allow for negative exponents of the indeterminate as long as these negative exponents are bounded ( here by k _ 0 ).
Where n and k _ 0 are a nonzero natural number and an integer respectively ( which are part of the datum of " f " ) : in other words, Puiseux series differ from formal Laurent series in that they allow for fractional exponents of the indeterminate as long as these fractional exponents have bounded denominator ( here " n " ), and just as Laurent series, Puiseux series allow for negative exponents of the indeterminate as long as these negative exponents are bounded ( here by k _ 0 ).
In other words, the field of Puiseux series with coefficients in " K " is the union of the fields K ( \ ! ( T ^ { 1 / n } ) \ ! ) ( where " n " ranges over the nonzero natural numbers ), where each element of the union is a field of formal Laurent series over T ^ { 1 / n } ( considered as an indeterminate ), and where each such field is considered as a subfield of the ones with larger " n " by rewriting the fractional exponents to use a larger denominator ( e . g ., T ^ { 1 / 2 } is identified with T ^ { 15 / 30 } ).

fractional exponent การใช้

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