Quick notation+statement verification

  • Thread starter bomba923
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732
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Do you agree that, [tex] \forall k \in \left[ {a,b} \right]\;{\text{where}}\;\left( {a,b,k} \right) \in \mathbb{Q}^3 [/tex],
[tex] \exists \,\varepsilon > 0{\text{ such that}}\;\forall n \in \mathbb{N},\;\left( {\left\{ {k_1 ,k_2 , \ldots ,k_n } \right\} - a} \right) \subseteq \varepsilon \left\{ {0,1,2, \ldots ,\left\lfloor {\frac{{b - a}}{\varepsilon }} \right\rfloor } \right\} [/tex]

|*Is this True or False ?
 
Last edited:

matt grime

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i don't think it makes sense until you say what the k_n are. don't bother with the symbols just write it in english.
 
732
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Sorry:redface:; the whole mess seems to simplify down to this statement:

[tex] \forall \left\{ {k_1 ,k_2 , \ldots ,k_n } \right\} \subset \mathbb{Q}\;{\text{where }}k_1 < k_2 < \ldots < k_n , [/tex]
[tex] \exists \,\varepsilon > 0\;{\text{such that}}\;\forall n \in \mathbb{N},\;\left\{ {k_1 ,k_2 , \ldots ,k_n } \right\} \subseteq \varepsilon \left\{ {0,1,2, \ldots ,\left\lfloor {\frac{{k_n - k_1 }}
{\varepsilon }} \right\rfloor } \right\} [/tex]

*|is this True or False?
 
Last edited:

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