Question about a logic notation

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The discussion centers on the interpretation of the logic notation (x∈R → f(x)>0) → f is asmani. Participants explore whether this means that if there exists some x in R such that f(x) > 0, then f is considered "asmani," which is humorously noted to mean "sky" in Persian but is suggested to imply "always positive." Clarification is sought on whether this is a common mathematical formulation, with one participant affirming that it is a standard definition, similar to stating that a matrix is positive definite if certain conditions are met. The conversation also touches on the meaning of "armani" in Persian, which translates to "ideal." Overall, the thread highlights the ambiguity in the term "asmani" and its mathematical implications.
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(x∈R → f(x)>0) → f is asmani.

What does it mean:

1. If there exists some x in R such that f(x)>0, then f is asmani.

2. If for all x in R we have f(x)>0, then f is asmani.

3. It's ambiguous or meaningless.

4. ...?

Thanks in advance.
 
Last edited:
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asmani said:
(x∈R → f(x)>0) → f is asmani

2. If for all x in R we have f(x)>0, then f is asmani. :smile:
 
And now I am going to spend all day wondering what "asmani" means!
 
tiny-tim said:
2. If for all x in R we have f(x)>0, then f is asmani. :smile:
Thanks. Is that a common formulation?
HallsofIvy said:
And now I am going to spend all day wondering what "asmani" means!
asmani means skiey (or of sky) in Persian, although I didn't mean that!
 
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I think it means always positive. Frankly, I have never seen that word.
 
asmani said:
Thanks. Is that a common formulation?

not sure i understand you :confused: …

that is the only interpretation of your original formula :smile:​
asmani means skiey (or of sky) in Persian, although I didn't mean that!

haha! :biggrin:

as a matter of interest, does "armani" mean anything in Persian?
 
tiny-tim said:
not sure i understand you :confused: …

that is the only interpretation of your original formula :smile:​
No, I mean the original formula. Is it a common formula in order to say "If for all x in R we have f(x)>0, then f is asmani"
I mean the original formula. Is that a common formulation in order to say "If for all x in R we have f(x)>0, then f is asmani"?
tiny-tim said:
haha! :biggrin:

as a matter of interest, does "armani" mean anything in Persian?
Yes, it means "ideal". :smile:
 
asmani said:
I mean the original formula. Is that a common formulation in order to say "If for all x in R we have f(x)>0, then f is asmani"?

yes, that is a standard form of definition

eg: "if, for all non-zero vectors x, xTAx > 0, then A is positive definite" :wink:
 

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