continuum hypothesis

Continuum Hypothesis

Proposed by Georg Cantor in 1878 while studying different sizes of infinity. It asks whether there exists a size of infinity between:

Countable infinity (N, Z, Q)

· elements listable one by one · like the pixels of a digital image

Uncountable infinity (R)

· continuous values · like the tones in an analog photo

Continuum Hypothesis for Photography

D = {digital images}
A = {analog photographs}
∃ x : D < x < A ?

Gödel (1940) proved that it cannot be disproved. Cohen (1963) proved that it cannot be proved either.

Thus the question remains undecidable.