Doppler Effect Disproves Einstein's Relativity

Doppler effect - when an observer moves toward a stationary source https://www.youtube.com/watch?v=bg7O4rtlwEE

The University of Texas at Austin: "Thus, the moving observer sees a wave possessing the same wavelength [...] but a different frequency [...] to that seen by the stationary observer." http://farside.ph.utexas.edu/teachin...ml/node41.html

This implies that the moving observer sees a different speed of light, in accordance with the formula

(frequency) = (speed of light)/(wavelength)

The University of Texas at Austin would have saved Einstein's relativity if they had written:

"The moving observer sees a wave possessing a different frequency to that seen by the stationary observer, and a wavelength shift inversely proportional to the frequency shift."

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