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Background:

Definition: An element $a\in R$ is an associate of $b\in R$ provided $a=bu$ for some unit $u.$

Questions:

I want to ask in math notation, to say that $a$ is not an associate of $b$ means that for every unit $u$, $a\neq bu$ Is that the correct negation?

Thank you in advance

KReiser
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Seth
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  • Yes it is correct – Kroki Feb 05 '24 at 03:22
  • @Kroki ah kk. Thank you. – Seth Feb 05 '24 at 03:23
  • But that is not "notation"... – Arturo Magidin Feb 05 '24 at 03:38
  • @ArturoMagidin i don't know what to call it. – Seth Feb 05 '24 at 03:39
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    You are asking about the negation/meaning of the term, not about how to represent it symbolically (which is what "notation" is). In particular, note the description of the notation tag: "Questions on the meaning, history, and usage of mathematical symbols and notation. Please remember to mention where (book, paper, webpage, etc.) you encountered any mathematical notation you are asking about." You are not asking about any of that. – Arturo Magidin Feb 05 '24 at 04:29
  • @ArturoMagidin I edited the title of my post. – Seth Feb 05 '24 at 04:31
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    This is a question about propositional calculus, i.e. how to negate an existential statement. It is expected that one already knows such basic logic before studying abstract algebra, so you may be trying to run before you have learned to walk. – Bill Dubuque Feb 05 '24 at 06:08
  • @BillDubuque I have taken courses in symbolic logic. I don't think doing thousands of different translation exercises is going to help me with language issues in abstract algebra. i never had much trouble with real or complex analysis. There is something about the précision of language thar trips me up in algebra. – Seth Feb 05 '24 at 06:15
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    It's because the objects tend to be more abstract here than in calculus so you are forced to rely on symbolic reasoning rather than less rigorous (geometric) intuition. – Bill Dubuque Feb 05 '24 at 06:33
  • @BillDubuque wait, so real, complex and functional analysis including point set topology are geometric on nature compare to abstract algebra? I just find the définitions in abstract algebra, I find sometimes the definition difficult to translate to symbolic logic notations. – Seth Feb 05 '24 at 06:37
  • Your said real/complex analysis above, not point set topology. It is quite common to hear students complain that they have much more difficulty developing intuition for algebra vs. analysis. – Bill Dubuque Feb 05 '24 at 06:49
  • @BillDubuque I saw in an interview where Terrence Tao said it took him à while to wrap his head around algebra and topology. I don't feel so bad after hearing that. – Seth Feb 05 '24 at 06:57
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    Evolution didn't wire our brains for such very abstract reasoning. We have to do that on our own. – Bill Dubuque Feb 05 '24 at 06:59
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    Please stop using MathJax to format text. Use markdown instead. – KReiser Feb 08 '24 at 05:26
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    @Seth, Bill Dubuque is trying to help you. From the other post I helped you with, it's clear that applying logical operations to text troubles you. It doesn't need to. I would take his suggestion at face value, and spend a few hours ironing out troubles in stating propositions, their converses, negations, contrapositives, etc. Your life will get easier. – RobinSparrow Feb 08 '24 at 05:56

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