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I was thinking of the division by zero that is impossible because you can’t divide a number in $0$ parts. But then I was thinking that is the same with multiplication, you can’t multiply a number $0$ times. Am I correct?

Witzig Adrien
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    $$0\cdot x=x\cdot 0=0.$$ –  Sep 13 '20 at 13:36
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    If somebody takes all your money, your money gets multiplied by $0$. – markvs Sep 13 '20 at 13:37
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    Your title seems asks about multiplication by $0$, but the body of your question asks about multiplying a number $0$ times, which is different from multiplying a number times $0$ – J. W. Tanner Sep 13 '20 at 13:48

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If we are speaking about, for example, real numbers $\mathbb{R}$, then multiplication, as we know, is paired with its inverse operation division. For division from scratch we want, that for $a,b$ there $\exists c$, such that $\frac{a}{b}=c$, means $b\cdot c=a$. But when we come to case with $b=0$, then we have contradiction: If $a \ne 0, b=0$, then from $\frac{a}{0}=c$ we have $0\cdot c=a$ and we obtain contradiction $a=0$, so you cannot divide non zero $a$ in $0$ parts, as we want keep $0\cdot c=0$ for any $c \in \mathbb{R}$.

So exactly fact that we can multiply number $0$ times, prevent dividing $0$ times.

There is generalization of this situation: in abstract algebra in rings element $a$ is called left divisor of zero, when $\exists b \ne 0$ such that $ab=0$. For initial info you can look at Zero divisor.

zkutch
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Basically what your asking is: what is for example $3^0$ which is multiplying by $3$, $0$ times. Well the answer is $1$.

$0^0$ is a special case which is undefined.

zooby
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