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UnkleRhaukus
 2 years ago
\[(\forall n\in \mathbb Z)[nn^2]\]
UnkleRhaukus
 2 years ago
\[(\forall n\in \mathbb Z)[nn^2]\]

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ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2What does "" mean in logic?

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2The division thing? Yes.

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2What if \(\rm n = 0\)?

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2Though the statement is true for \(\mathbb{Z}^+\)

joemath314159
 2 years ago
Best ResponseYou've already chosen the best response.1Dont read :\[n\mid n^2\]as division. By definition, \[a\mid b \iff b=ak ,k\in \mathbb{Z}\]there is no division taking place. By this definition, 0 does divide 0^2 since 0^2=0*0

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2I've always heard, zero cannot divide anything.

joemath314159
 2 years ago
Best ResponseYou've already chosen the best response.1You are thinking of fractions. Notice the definition doesnt contain anything about fractions.

joemath314159
 2 years ago
Best ResponseYou've already chosen the best response.1its a statement only about multiplication.

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0\[ab \iff \exists q[b=aq],a\neq 0\]

joemath314159
 2 years ago
Best ResponseYou've already chosen the best response.1ah, then i am mistaken. if a cant be zero then what i posted is wrong.

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2So, in fact, we do have fractions in the definition.

joemath314159
 2 years ago
Best ResponseYou've already chosen the best response.1hmmm, i still wouldnt say there are fractions. This is generally the way they talk about division in Rings, where only multiplication and addition are defined. But yes, a cannot be zero. http://primes.utm.edu/glossary/xpage/divides.html

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0\(ab\) denotes \(b\) is divisible by \( a \)
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