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

  • #1
398
47
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.
 

Answers and Replies

  • #2
andrewkirk
Science Advisor
Homework Helper
Insights Author
Gold Member
3,860
1,438
I have never come across any distinction between 'holds' and 'holds true'. They are both just ways of saying 'it is the case'.
 
  • #3
398
47
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?
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,833
956
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.
 
  • #5
398
47
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.
 
  • #6
QuantumQuest
Science Advisor
Insights Author
Gold Member
926
485
"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.
 

Related Threads on What is different between "holds" and "holds true"?

Replies
4
Views
748
Replies
1
Views
1K
Replies
13
Views
3K
Replies
7
Views
4K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
20
Views
3K
Top