QuantizationBitRate

PCM Quantization bit rate and cardinality

Quantization bit rate (bit)	Cardinality
1	2
8	256
16	65536
24	16777216
32	4294967296
48	281474976710656
64	18446744073709551616
128	340282366920938463463374607431768211456
256	115792089237316195423570985008687907853269984665640564039457584007913129639936
ℵ0 (countably infinite)	ℵ1 (cardinality of the continuum) ※

Therefore, if quantization bit rate is increased to countably infinite, any real number (rational numbers and irrational numbers) can be expressed exactly.

※……There is the following relation among with those two infinite cardinalities: 2^{ℵ0} ＝ ℵ1