Question

\[(\forall n\in \mathbb Z)[n|n^2]\]

Answer 1

t/f

Answer 2

What does "|" mean in logic?

Answer 3

divides

Answer 4

The division thing? Yes.

Answer 5

Except for 0.

Answer 6

True

Answer 7

What if \(\rm n = 0\)?

Answer 8

n^2=n*n
so (n*n)/n=n

Answer 9

False.

Answer 10

Truesomeness

Answer 11

Though the statement is true for \(\mathbb{Z}^+\)

Answer 12

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

Answer 13

I've always heard, zero cannot divide anything.

Answer 14

You are thinking of fractions. Notice the definition doesnt contain anything about fractions.

Answer 15

its a statement only about multiplication.

Answer 16

Oh.

Answer 17

\[a|b \iff \exists q[b=aq],a\neq 0\]

Answer 18

ah, then i am mistaken. if a cant be zero then what i posted is wrong.

Answer 19

So, in fact, we do have fractions in the definition.

Answer 20

hmmm, 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

Answer 21

\(a|b\) denotes \(b\) is divisible by \( a \)