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I just missed the obvious context -- finite time writing <<what>> exactly. The exceptions can be written in finite time using integers and a specific set of ope
by hansvm 5y ago
I just missed the obvious context -- finite time writing <<what>> exactly. The exceptions can be written in finite time using integers and a specific set of operations, whereas the question I posed looked at decimal representations.
- ncmncm 5y agoNo. In infinite time you can write a countably-infinite number of symbols, identifying a countably-infinite number of exceptions. You might choose to write some random set other than the rationals and roots, but what you could write (absent infinite repetition) would have exactly as many members as those sets, and thus map to them one-to-one; so, just identify them possibly more abstractly. But the set will in any case remain negligible vs. the uncountably-infinite real numbers.