Question

Unsure of this notation??

Answer 1

\[sgn (\frac{ a_{m} }{ b_{n} }) \infty\]

I know what the signum function is, but when a result is written liek this, I'm not sure how to interpret it.

Answer 2

Infinity can be positive or negative...

Answer 3

That's literally what it means, you can have \(\pm \infty\) ?

Answer 4

Signum takes a real to the following: \(\text{sgn} : \mathbb{R} \to \{1, -1\}\). So if the ratio is a negative number the result is negative infinity, and otherwise it is positive infinity.

Answer 5

Ah, so it's kind of like a multiplication by infinity then?

Answer 6

There is actually a formal definition of these operations. \(\infty\) can be thought of as a number and operated on in the extended reals. In this case \(-1\cdot \infty = -\infty\). Also probably by convention you will define \(0 \cdot \infty = 0\) and so on.

Answer 7

Yeah, I figure you usually don't do algebra with infinity, but if that's just a convention that can be done with these then sure, that works. Alright, thank you :)

Answer 8

http://en.wikipedia.org/wiki/Extended_real_number_line#Arithmetic_operations