indirect proof of identity theorem of power series
is valid in the set of points presumed in the theorem (http://planetmath.org/IdentityTheoremOfPowerSeries) to be proved.
Antithesis: There are integers such that ; let () be least of them.
But all the time, the left and of (2) are equal, and thus also the limits. So we must have , contrary to the antithesis. We conclude that the antithesis is wrong. This settles the proof.
Note. I learned this proof from my venerable teacher, the number-theorist Kustaa Inkeri (1908–1997).
|Title||indirect proof of identity theorem of power series|
|Date of creation||2013-03-22 16:47:48|
|Last modified on||2013-03-22 16:47:48|
|Last modified by||pahio (2872)|