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

[bacte2013]

Hello!

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.

 

[andrewkirk]

I have never come across any distinction between 'holds' and 'holds true'. They are both just ways of saying 'it is the case'.

 

[bacte2013]

I have never come across any distinction between 'holds' and 'holds true'. They are both just ways of saying 'it is the case'.

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?

 

[HallsofIvy]

Does that mean "theorem holds for all x in R" and "theorem hold true for all x in R" are the same?

Yes.

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?

No. The two phrasings mean exactly the same thing.

 

[bacte2013]

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?

Yes.No. The two phrasings mean exactly the same thing.

Thanks! Recently, I have been very nervous about the use of grammars.

 

[QuantumQuest]

"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.