Why is the electromagnetic spectrum continuous?

Because wavelength, frequency, or photon energy are continuous parameters that distinguish electromagnetic waves and photons from one another.

As an example, the visible portion of the spectrum has a wavelength that varies infinitely from 350 to 700 nanometers. Two orange-yellow lines emitted by sodium atoms are located in this range at 588.5924 and 589.9950 nanometers, respectively.

Similar to real numbers, the small range between 588.5924 nm and 589.9950 nm contains infinite wavelength values.

The spectrum is "potentially" continuous in this sense, encompassing a range of possible wavelength, frequency, and photon energy values.

A candle, a glowing wire, or a furnace emits a truly continuous spectrum, which implies that all possible electromagnetic radiation is actually emitted, with varying intensities, over a broad energy range.

The electromagnetic spectrum is continuous because electromagnetic waves can have a range of frequencies and wavelengths, allowing for a seamless transition between different types of waves. This continuity is a result of the continuous nature of electric and magnetic fields in the waves.