4 ms·

Whatever largest number you can express in your system, I can represent a larger one in only one bit, using the following specification. 0=your largest number

• deleted 8mo ago
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• Veserv 8mo ago
  To be pedantic, that is a instance of the Berry paradox [1] and no you can not [2] as that would be a violation of Godel's incompleteness theorems. edit: To clarify further, you could create a new formal language L+ that axiomatically defines 0 as "largest number according to L", but that would no longer be L, it would be L+. For any given language with rules at this level of power you could not make that statement without creating a new language with even more powerful rules i.e. each specific set of rules is capped, you need to add more rules to increase that cap, but that is a different language. [1] https://en.wikipedia.org/wiki/Berry_paradox https://en.wikipedia.org/wiki/Berry_paradox [2] https://terrytao.wordpress.com/2010/11/02/the-no-self-defeating-object-argument-and-the-vagueness-paradox/ https://terrytao.wordpress.com/2010/11/02/the-no-self-defeat...
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  • o_nate 8mo ago
    It's not a paradox, because there is nothing logically inconsistent in my definition, unlike the Berry paradox.
  • thewakalix 8mo ago
    To be more pedantic, yes you can, but only with a meta-language.