# Zero x infinity = -1 ?

## Main Question or Discussion Point

Zero x infinity = -1 ???!!!

when two lines meet perpendicularly, we hv the formula v
m1 x m2 = -1

if a horinzontal line meet v a vertical line,by using same formula ,we hv
m1 x m2 = -1
zero x infinity = -1

so..does it make sense??!! HallsofIvy
Homework Helper
bs said:
when two lines meet perpendicularly, we hv the formula v
m1 x m2 = -1

if a horinzontal line meet v a vertical line,by using same formula ,we hv
m1 x m2 = -1
zero x infinity = -1

so..does it make sense??!! No, "infinity" is not a real number. Saying that a vertical line has slope "infinity" is just a way of saying that a vertical line does not have a slope. (In fact, it would make just as much sense to say that a vertical line has slope "negative infinity".) There are a variety of numbers systems that include some notion of "infinity" but in those multiplication of a number by infinity is either not defined or gives something other than -1. I don't know of any number system that defines multiplication of zero by infinity to give -1.

Alkatran
Homework Helper
Multiplying 0 by infinity is like dividing 0 by 0, inderterminate. You can get any answer you want. For example:

1:
$$\lim_{x\rightarrow\infty} x * \frac{1}{x^2} = 0 * \infty$$
$$\lim_{x\rightarrow\infty} x * \frac{1}{x^2} = 0$$

$$0 * \infty = 0$$

2:
$$\lim_{x\rightarrow\infty} x * \frac{1}{x} = 0 * \infty$$
$$\lim_{x\rightarrow\infty} x * \frac{1}{x} = 1$$

$$0 * \infty = 1$$

3:
$$\lim_{x\rightarrow\infty} 2 * x * \frac{1}{x} = 0 * \infty$$
$$\lim_{x\rightarrow\infty} 2 * x * \frac{1}{x} = 2$$

$$0 * \infty = 2$$

Alkatran said:
Multiplying 0 by infinity is like dividing 0 by 0, inderterminate. You can get any answer you want. For example:

1:
$$\lim_{x\rightarrow\infty} x * \frac{1}{x^2} = 0 * \infty$$
$$\lim_{x\rightarrow\infty} x * \frac{1}{x^2} = 0$$

$$0 * \infty = 0$$

2:
$$\lim_{x\rightarrow\infty} x * \frac{1}{x} = 0 * \infty$$
$$\lim_{x\rightarrow\infty} x * \frac{1}{x} = 1$$

$$0 * \infty = 1$$

3:
$$\lim_{x\rightarrow\infty} 2 * x * \frac{1}{x} = 0 * \infty$$
$$\lim_{x\rightarrow\infty} 2 * x * \frac{1}{x} = 2$$

$$0 * \infty = 2$$

Amazing. Off the subject, but a comment nonetheless: Perhaps your examples demonstrates how "all things are possible"

Alkatran