[ertgbnm]

Yes it's easier and not too different from Turing's argument. However, Turing made this proof in 1936, you know, before the concept of pixels exists.

[tempfile]

Approximating an arbitrary shape by covering it with tiny squares is not exactly new. The method of exhaustion goes back to 200BC.

[Y_Y]

Not far off though, "pix" was in use by at least 1932, and "pixel" by 1956[0].

[0] https://en.wikipedia.org/wiki/Pixel

[throwawayffffas]

The Planck length has been a thing since 1899.

[kragen]

nyquist's sampling theorem is from 01915. western union started offering wirephoto service in 01921, and the associated press started mass distribution of news photos in 01935. these aren't discrete pixels but they did demonstrate that nyquist's sampling theorem applies to images too

[eru]

If you want to use that sampling theorem, you have to bring up frequencies. Explaining those and how they apply to printer's ink is arguably more complicated than what Turing did; especially for his contemporary target audience.

The argument from pixels is more natural to us these days, that's why we think it's simpler.

(I had similar reactions to many other older style proofs when I was studying math.)

[kragen]

fair point