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Firstly, I'm pretty sure I understand why $\frac{n}{0}$ is undefined.

Example

Into how many groups of zero could you separate n blocks?

Well, no matter how many zero's you sum up, you will never have $n$ blocks.

Multiplication is commutative, therefore any number $n\times0 = 0\times n = 0$.

There isn't a way to read left to right or right to left that would make any difference in the answer.

There is something that's not explained here.

For example,

$2\times 3$ could be $2+2+2$ or it could be $3+3$. The distinction isn't really important per say, regardless of what you choose it to be, your answer is always going to be the same.

However, multiplying by zero for instance, say

$5\times 0$ could be $0+0+0+0+0 = 0$ and $5\times 0 = 0\times 5$

It's not clear whether $5\times 0$ could be defined as $5$ zero times.

Given that $\frac{5}{0}$ is undefined, is $5\times 0 = 0+0+0+0+0$ the only way to interpret the product of $5\times 0$?

Is the only way to define a product $n\times 0$ that we have "$n$" zero's?

Andrés E. Caicedo
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Andrew
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  • you could think of $n\times0$ as $n$ zeroes or zero $n$s (the empty sum is zero) – J. W. Tanner Nov 19 '19 at 01:11
  • I get that the math works if you interpret n x 0 that way, what I'm asking is can you think of n x 0 as zero n's because it can also be read as "n" zeros, so that math works so we don't care about the real meaning. – Andrew Nov 19 '19 at 01:14
  • Good question! Another perspective is to view $0$ as almost like the base value (in more technical lingo, the identity) for addition. When you have nothing else, you are left with $0$. In multiplication, we have a similar base value, $1$. That's part of teh reason that $0!=1$. – Rushabh Mehta Nov 19 '19 at 01:55

1 Answers1

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If you have no five-dollar bills, how much money do you have? What if you have no hundred-dollar bills?

Unit
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