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This theorem blew my mind on the Set Theory 101. A particularly interesting implication is that we can't say anything about the vast majority of the real number
by t0mek 10y ago
This theorem blew my mind on the Set Theory 101. A particularly interesting implication is that we can't say anything about the vast majority of the real numbers. Anything we say or write, all texts created by the humanity now and in the future creates a countable set. Since the real numbers are not countable, we can't assign them with the definitions.
- sdenton4 10y agoFor some added fun: algebraic numbers are the set of all numbers which are roots of rational polynomials. You know, things like sqrt 2, along with all the rationals themselves. Algebraic numbers comprise the vast majority of real numbers we ever have a reason to actually use. These are also merely countable...
- petters 10y agot0mek noted that all possible definitions of a number are countable. That would include all algebraic numbers.
- effie 10y ago> we can't say anything about the vast majority of the real numbers. It depends on which majority is at question. For that majority that is irrational, we can say any member can be approximated arbitrarily closely by a rational number.