zero multiplied by infinity

[gonelli]

This was an idea that i came up with during a math class, where we were learning about perpendicular lines. The way to prove/solve perpendicular lines is by multiplying the gradient of the first line by the second gradient and the answer will be -1.

So i had the though that a flat horizontal line has a gradient of 0, and a perfectly vertical line is described as "undifined". Now because the line is undifined i thought that would mean it can be described as infinity. So that would mean that 0 (flat line) multiplied by infinity (vertical line) equals -1.

Tell me what you think.

[D H]

Similar arguments can be made regarding the value of 0*infinity and any other number. I could argue that 0*infinity is -1, 0, 1, 1.5, or any other number. This is why we must say that 0*infinity is undefined.

[insane_alien]

is it positive or negative infinity?

[timo]

That would depend on whether it´s positive or negative zero

[YT2095]

zero multiplied by infinity = Zero OR One

 

 

(in my opinion)

[John Cuthber]

In my opinion it's 42 this week but it will be a bit bigger next week, shrinking slowly after Easter; fortunately my opinion doesn't count for much.

 

0* infinity =42

Multiply both sides by zero (an odd opperation for a mathematician, but sort of legitimate. Division by zero is forbidden, not multiplication) and get

0*0*infinity=0

 

0*0=0 so I can simplify the first term and get

0*infinity =0

(zero squared really is zero; this simplification is legitimate)

 

OK, that's one of the values you accept so we agree.

This is an amusing game but contributes little to mathematics so those in charge simply banned it. Division by zero (and the equivalent multiplication by infinity) are not defined.

[sinisterwolf]

Well the division by zero isn't entirly forbiden. For example if you're working with an equation that as an aymtote, i.e. (x^2)+4/(x^2)-4, clearly if you plug 2 into that euation you will get 8/0, undefined?, no it is Infinity because the closer you get the (x^2)=4 the greater the number gets, there fore a number divided by zero is infinity given you are working with a function.

[sinisterwolf]

For give me I haven't exatly figured out the system of writing math on these threads so I hope you can understand what I wrote.

[Sisyphus]

Well the division by zero isn't entirly forbiden. For example if you're working with an equation that as an aymtote, i.e. (x^2)+4/(x^2)-4, clearly if you plug 2 into that euation you will get 8/0, undefined?, no it is Infinity because the closer you get the (x^2)=4 the greater the number gets, there fore a number divided by zero is infinity given you are working with a function.

 

That's not something divided by zero. That's something divided by a quantity which approaches zero (meaning it decreases without limit), which is that it approaches infinity (meaning it increases without limit).

[Dave]

This is an amusing game but contributes little to mathematics so those in charge simply banned it. Division by zero (and the equivalent multiplication by infinity) are not defined.

 

Pretty much. I dislike discussions of this sort quite a lot, because I feel that in order to really talk about 'infinity' you should have some vague concept of a limit, and what it means for a function to be unbounded at some point. Unfortunately unless you've taken a introductory course in real analysis this probably isn't going to happen.

 

It is possible and indeed very useful to consider points that are labelled as infinity; for example, the extended reals or projective space. However, this is done quite carefully. For anyone interested in this, I suggest studying some complex analysis and taking a look at the Riemann sphere, which is possibly one of the more simple examples.