Even though there is a non-denumerable number of real numbers, there is only a denumerable number of them we can represent in a finitary logic. The real numbers which we can represent can be set to a one to one correspondence to the rational numbers, or even just the natural numbers. <\/p>\n
But we have an intuitive knowledge of infinity and continuity that goes beyond discrete finitary intellect. <\/p>\n
There are multiple such dualities.<\/p>\n
Discrete — Continuous
\nParticle — Wave
\nIntellect — Intuition
\nDigital — Analog
\nOpaque — Ambiguous (???) Added 9\/17\/2013<\/p>\n
Each of these has its place.
\nI have talked to those who think quantum mechanics indicates everything comes in discrete quanta. It is true that the energy of a photon of a specific frequency has a fixed energy (E = h v), but the frequency (v) can vary continuously. <\/p>\n","protected":false},"excerpt":{"rendered":"
Even though there is a non-denumerable number of real numbers, there is only a denumerable number of them we can represent in a finitary logic. The real numbers which we can represent can be set to a one to one correspondence to the rational numbers, or even just the natural… Continue reading