think about this
$${\mathtt{\,-\,}}{\frac{{\mathtt{9}}}{{\mathtt{0.1}}}} = -{\mathtt{90}}$$
$${\mathtt{\,-\,}}{\frac{{\mathtt{9}}}{{\mathtt{0.01}}}} = -{\mathtt{900}}$$
$${\mathtt{\,-\,}}{\frac{{\mathtt{9}}}{{\mathtt{0.001}}}} = -{\mathtt{9\,000}}$$
$$\frac{-9}{n}\quad \mbox{ approaches} -\infty \mbox{ as n }\rightarrow\: ^+0$$
BUT n can approach 0 from above or below.
$${\mathtt{\,-\,}}{\frac{{\mathtt{9}}}{-{\mathtt{0.1}}}} = {\mathtt{90}}$$
$${\mathtt{\,-\,}}{\frac{{\mathtt{9}}}{-{\mathtt{0.01}}}} = {\mathtt{900}}$$
$${\mathtt{\,-\,}}{\frac{{\mathtt{9}}}{-{\mathtt{0.001}}}} = {\mathtt{9\,000}}$$
This time
$$\frac{-9}{n}\quad \mbox{ approaches} +\infty \mbox{ as n }\rightarrow\: ^-0$$
n cannot approach -infinity and +infinity at the same time and end up at the same place so -9/0 must be undefined. I think indeterminant is the more common term these days but to the best of my understanding both terms mean the same thing.
Does that make sense to you?
-9/0
-9/1 ÷ 0/0
-9/1 * 0/0
-0/0
= 0
I'm not entirely sure if this is correct because I tried it on two different calculators. One said ERROR and the other one said -Infinity.
...?
Any number divided by 0 (zero) is undefined. This includes 0/0.
It is NOT infinity nor negative infinity.
The calculator that returned "-Infinity" is wrong!
think about this
$${\mathtt{\,-\,}}{\frac{{\mathtt{9}}}{{\mathtt{0.1}}}} = -{\mathtt{90}}$$
$${\mathtt{\,-\,}}{\frac{{\mathtt{9}}}{{\mathtt{0.01}}}} = -{\mathtt{900}}$$
$${\mathtt{\,-\,}}{\frac{{\mathtt{9}}}{{\mathtt{0.001}}}} = -{\mathtt{9\,000}}$$
$$\frac{-9}{n}\quad \mbox{ approaches} -\infty \mbox{ as n }\rightarrow\: ^+0$$
BUT n can approach 0 from above or below.
$${\mathtt{\,-\,}}{\frac{{\mathtt{9}}}{-{\mathtt{0.1}}}} = {\mathtt{90}}$$
$${\mathtt{\,-\,}}{\frac{{\mathtt{9}}}{-{\mathtt{0.01}}}} = {\mathtt{900}}$$
$${\mathtt{\,-\,}}{\frac{{\mathtt{9}}}{-{\mathtt{0.001}}}} = {\mathtt{9\,000}}$$
This time
$$\frac{-9}{n}\quad \mbox{ approaches} +\infty \mbox{ as n }\rightarrow\: ^-0$$
n cannot approach -infinity and +infinity at the same time and end up at the same place so -9/0 must be undefined. I think indeterminant is the more common term these days but to the best of my understanding both terms mean the same thing.
Does that make sense to you?
Ooooops I must be confusing with this $$\lim\limits_{x \to 0}{\frac{c}{x}} = \infty$$ $$c = const$$. Really sorry, I'm just hooked on maths analysis recently.