mathematical theory

[Psyk]

I remember bumping into Alphanumeric on another forum. Didn't find out why he was banned from here though.

 

[growse]

Any number divided by zero is technically... infinity.

Think about it, and it'll make sense. It's impossible to reach this result in our reality so this is why we cannot allow a division by zero.

If you perform any division, if the second operand is below 1, the closer it gets to 0, the higher the result. Tending toward zero raises the result higher exponentially.

Funny when I was studying I always used to have this thought about dividing a number by 2, then dividing it again, and again, and again etc. I concluded that it would take an infinite amount of time to eventually get a result of 0, so you can never finish this operation.

Tends to != is the same as.

1/x -> infinity as x -> 0. However, it is illogical to make the leap that 1/0 is therefore infinity. It's undefined. Ask anyone who's actually an expert in maths.

 

[DaveF]

Tends to != is the same as.

1/x -> infinity as x -> 0. However, it is illogical to make the leap that 1/0 is therefore infinity. It's undefined. Ask anyone who's actually an expert in maths.

Of course, with the standard one point compactification of the real line, 1/0 is indeed infinity. (Or, if memory serves, the compactification of the complex plane to form a Riemann Sphere, for that matter).

 

[Duff-Man]

Of course, with the standard one point compactification of the real line, 1/0 is indeed infinity. (Or, if memory serves, the compactification of the complex plane to form a Riemann Sphere, for that matter).

moebius transformations... yeah. I vaguely remember that all stuff I was always more into the applied math though.

Anyway, when the complex plane compactifies to a sphere, every point on the sphere has a unique corresponding point on the complex plane - Except for the top of the sphere, which represents "the infinite boundary" of the complex plane. Technically, this point in the compactified sphere is also undefined.

 

[DaveF]

moebius transformations... yeah. I vaguely remember that all stuff I was always more into the applied math though.

Anyway, when the complex plane compactifies to a sphere, every point on the sphere has a unique corresponding point on the complex plane - Except for the top of the sphere, which represents "the infinite boundary" of the complex plane. Technically, this point in the compactified sphere is also undefined.

I admit I'm having to look it up on Wiki, as it's 20 years since I did this, but to my understanding, it's perfectly well defined in the "2nd atlas" of the Riemann Sphere. (Not that this matters in terms of one-point compactification, but it's kind of handy if you want to be able to claim that 1/0 = infinity afterwards).

 

[growse]

Of course, with the standard one point compactification of the real line, 1/0 is indeed infinity. (Or, if memory serves, the compactification of the complex plane to form a Riemann Sphere, for that matter).

Yes, but all bets are off when you start bending the number plane