Recent content by eabod

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    First order logic: definability

    On one hand you said you don't know what it means for a subset of \mathbb{R}\times \mathbb{R} to be definable, yet here you've (correctly) explained what it means and even given an example of one, namely \{ (x,y) \mid x<y\}. Thus I will assume that you do know what it means for for a subset of...
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    First order logic: definability

    The language doesn't include "and", "or" or "=", since those are covered by the (language of the!) underlying logic, which in this case I assume is first order logic (with equality). In model theory, when one speaks of "language", the underlying logic will already have been established, so...
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    Linear algebra(linear transformation)

    I think the rank-nullity theorem is exactly what you want to use.
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    Graduate Archimedean property for unbounded sets

    Unbounded sets of what type of elements? Real numbers? I think you should reword or provide more details of your question and maybe even cite the text you're referring to (including page number, theorem number, etc.).
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    Graduate Understanding Logical Statements: P(x) and Q(x) in Z | Examples and Explanation

    I doubt if my response below says anything that your textbook/professor hasn't said, so your misunderstanding seems likely to be a symptom of a lack of reading/listening (and thinking about what you've read/heard). Learning to read/listen to mathematics takes work, but is invaluable (even...