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What is different between "holds" and "holds true"?

  1. Dec 11, 2015 #1

    I am currently studying the analysis, and I have a quick question. Whenever i claim (in proof) that a statement P holds for some x in R, can I assume that P holds true for some arbitrary numbers in R but not for all possible numbers in R? What is a difference between the terms "holds" and "holds true"? I know this is a subtle problem, but I am actually quite confused about it.
  2. jcsd
  3. Dec 11, 2015 #2


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    I have never come across any distinction between 'holds' and 'holds true'. They are both just ways of saying 'it is the case'.
  4. Dec 14, 2015 #3
    Does that mean "theorem holds for all x in R" and "theorem hold true for all x in R" are the same? Does the word "hold" contain any possibility of leaving a possibility of a theorem to be not true for all X in R, while "holds true" definitely assume the truth of the theorem?
  5. Dec 14, 2015 #4


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    No. The two phrasings mean exactly the same thing.
  6. Dec 14, 2015 #5
    Thanks! Recently, I have been very nervous about the use of grammars.
  7. Dec 14, 2015 #6


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    "Holds" and "Holds true", is definitely the same as said. Whatever has to be expressed about which members of a set satisfy a particular property, is done so explicitly using quantifiers or proper phrasing.
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