UnkleRhaukus
\[(\forall n\in \mathbb Z)[n|n^2]\]
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UnkleRhaukus
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t/f
ParthKohli
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What does "|" mean in logic?
joemath314159
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divides
ParthKohli
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The division thing? Yes.
ParthKohli
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Except for 0.
swissgirl
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True
ParthKohli
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What if \(\rm n = 0\)?
swissgirl
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n^2=n*n
so (n*n)/n=n
ParthKohli
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False.
swissgirl
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Truesomeness
ParthKohli
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Though the statement is true for \(\mathbb{Z}^+\)
joemath314159
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Dont 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
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I've always heard, zero cannot divide anything.
joemath314159
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You are thinking of fractions. Notice the definition doesnt contain anything about fractions.
joemath314159
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its a statement only about multiplication.
ParthKohli
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Oh.
UnkleRhaukus
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\[a|b \iff \exists q[b=aq],a\neq 0\]
joemath314159
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ah, then i am mistaken. if a cant be zero then what i posted is wrong.
ParthKohli
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So, in fact, we do have fractions in the definition.
UnkleRhaukus
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\(a|b\) denotes \(b\) is divisible by \( a \)