Isn't this notation a bit sloppy? I've done some mathematical logic in the past (although never connected to any form of analysis) and commas aren't even part of the alphabet of predicate logic.
Shouldn't this be expressed as:
[math]\forall x\exists y[(x, y \in \R) \to (y^3 = x)][/math]
(or possibly even more explicitly by not combining the membership of x and y in the antecedent but instead using an and statement)?
>>9104686
the picture didnt claim it was using predicate logic.
>>9104689
Then what logic is it using? I mean it has all the regular connectors, and, or, implication, negation, as well as the two quantifiers used in predicate logic.
>>9104686
>commas aren't even part of the alphabet of predicate logic
The truth is that everyone uses their own slightly different notation to suit their taste. There isn't a real Standard Notation that this here is violating.
>>9104717
it's just stating a fact. This notation let's you express it more succinctly. You should just read it as a sentence. And yeah, they omit the "such that" part. I'd put a "s.t" just to make it explicit.
>>9104686
What does the \ in front of R represent?
>>9106083
Thats a shortcut in Latex to get the fancy capital R for Real Numbers R
Why do they say it is true with no proof
>>9104686
what you have written is not equivalent to what is in the provided picture. indeed, as >>9104750 stated, this notation/use of quantifiers is simply a shorthand for expressing claims or statements about whatever you'r studying, in this case it appears like real analysis maybe or just introduction to proofs?
for all x in R, there exists y in R s.t. x = y^3. the comma doesn't necessarily make it wrong but it's pretty kitschy.
can someone explain this letter by letter?
looks interestin but i dont know any notation lmfao
>>9104686
You should just think of it as a sentence.
Besides logic autists, nobody cares about using exact set theoretic syntax.