# Why does the position operator have continuous spectra?

I am new to QM and was wondering how it is deduced that the position operator has a continuous spectrum of eigenvalues and eigenvectors. In particular, is the equation $$\hat{x}|x\rangle=x|x\rangle$$ taken to be a principle / postulate of QM or does this equation pop out as a consequence of something?

Also, does writing the eigenvalue equation for the position operator as above mean that the eigenvectors of the position operator are non-degenerate, say in 1D?