Question

Question #edcd2

Answer 1

No. A number "divided" by zero is "undefined". It does not have a numerical meaning.

Explanation:

The other way around, `0/4` is zero. But, while other expressions can be conceived as "infinity", the division by zero is simply - we don't know. It is undefined, and we cannot assign a numeric value to it.

Answer 2

It is a massive headache, we do not speak of this menace that you call "division by zero." Anything divided by zero is "undefined" - it doesn't have a value, you can't plot it. Its fairly complicated, but here's why:

Explanation:

Without dividing by zero, the closest we can do is to divide by smaller and smaller numbers which get closer and closer to zero. In other words, we are saying `4/0=lim_(n->0)(4/n)`
(4 divided by zero equals the limit as n approaches zero of 4/n)

Let:

`n=1, 4/n=4`
`n=0.1, 4/n=40`
`n=0.01, 4/n=400`
`n=1xx10^-6,` (one millionth), `4/n=4xx10^6` (4 million)

The values in between these and lower than a millionth are left as an exercise to the reader, but we can see a trend, it's getting bigger and bigger and closer to infinity. All good right, `lim_(n->0)(4/n)=oo`?

In the above example, we were starting (relatively) high, and coming down to zero. Perhaps we should write this as `4/0=lim_(n->0^+)(4/n)` (as n approaches positive zero)
We can also take the limit at 'negative zero' going up from the negative numbers:
`4/0=lim_(n->0^-)(4/n)`
We should get the same answer, right? They are both equal to 4/0.

`n=-1, 4/n=-4`
`n=-0.1, 4/n=-40`
`n=-0.01, 4/n=-400`
`n=-1xx10^-6, 4/n=-4xx10^6`

Again, other values are left as an exercise, but we can see that `4/0=lim_(n->0^-)(4/n)=-oo`

Both of these are equal to `4/0`. Wait, does that mean that `-oo=+oo`??? But that doesn't make sense!

If that doesn't give you enough of a head, we can do the same for other numbers. Take any positive real number - `1,4,7, sqrt2, e, pi, 1000` - the same trend holds true (for negatives, the opposite is the case, since dividing negative by a positive is negative, and negative divided by negative is positive).

So:

From the process above, `4/0=7/0`. (you can prove the same for 7/0 as we did for 4/0)

`4/0=7/0`
`:. 4=7` ?????????

But that can't be right. 4 isn't 7!!!

So, paradoxes and weird outcomes nobody likes is the reason dividing by zero is undefined. It HAS no definition. So you can't plot it on a number line.