Re: Calculus XOR Probability

Tony Orlow wrote:
Matt Gutting said:
Tony Orlow wrote:
Virgil said:
<snip>

If f(2) and g(2) are both defined, how can this be unless 2 is in the domain of both?
Unless the set generated by applying f to the naturals contains 2, 2 will not be a value used as a parameter to g. It need not be in S, which is the domain of g. However, this means g(2) is not a natural. It's still a real number. :)
If 2 is not in S, and S is the domain of g, then g(2) is not defined. A function
is only defined over its domain.

Matt

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The domains and codomains of the functions f and g are R. That means f(x) for x in R returns a y in R as a result. If N is a proper subset of R then S will also be a proper subset of R, because for every unique r in R but not in N there is a unique f(r) in R but not in S. g(2) will always be defined, but may not be in N. If that's the case, then 2 isn't in S. That's very basic. Doesn't anyone get this? I know I'm not crazy. Am I dreaming?

Perhaps I'm confused, but I appear to see a line in the text above which seems
to have been written by you and which says "S ... is the domain of g".

Matt

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Relevant Pages

  • Re: Calculus XOR Probability
    ... Tony Orlow wrote: ... Unless the set generated by applying f to the naturals contains 2, ... also be a proper subset of R, because for every unique r in R but not in N ... Tony knows so many things that are no so, perhaps he is dreaming. ...
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  • Re: Calculus XOR Probability
    ... Tony Orlow wrote: ... Unless the set generated by applying f to the naturals contains 2, 2 will not be a value used as a parameter to g. ... The domains and codomains of the functions f and g are R. That means ffor x in R returns a y in R as a result. ... If N is a proper subset of R then S will also be a proper subset of R, because for every unique r in R but not in N there is a unique fin R but not in S. gwill always be defined, but may not be in N. If that's the case, then 2 isn't in S. That's very basic. ...
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