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The DB,

   Sorry, not true at all.  Don't confuse radiation resistance with impedance.

Use a 1/2 wave length antenna that's resonant.  If fed in the center the input impedance should be in the neighborhood of 50 - 75 ohms.  If fed at one end, that input impedance will be in the neighborhood of 1000+ ohms.  The radiation resistance of that 1/2 wave length antenna has not changed, neither has it's resonance.

How about the input impedance of a 5/8 wave vertical antenna?  It's input impedance isn't 50 ohms by any means until it's been matched by an impedance matching device of some kind.

That radiation resistance is -part of- input impedance and it's value is almost never 50 ohms or really close.

 - 'Doc