All conditions are true for a certain range

  • Thread starter Hypercubes
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  • #1
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How do you specify, in mathematical notation, that a condition is true for all cases?

For example, I want to say that [tex]t=5[/tex] for every value of [tex]n[/tex]. Basically like [tex]\lim_{n\to\infty}{t=5}[/tex], but instead for every value of [tex]n[/tex], not just as [tex]n[/tex] approaches infinity. Also, how to specify the range of [tex]n[/tex] values for which the condition is true?

Thanks in advance.
 

Answers and Replies

  • #2
Char. Limit
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Well, we have the symbol ∀, which means "for all".

So you would say...

t=5 ∀n
 
  • #3
HallsofIvy
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I assume that is an example- it doesn't make sense to say that a statement, that does not involve n, is "true for all n".

But just "for all n, [itex]n^2\ge 0[/itex]" will work or, as Char limit said, ∀n, [itex]n^2\ge 0[/itex].
 
  • #4
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Yeah, it was just an example.

Thanks for the help!
 

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