Is infinity times 0 indeterminate?

[Realintruder]

The answer is yes!

 

infinity*0= infinity (1-1)=infinity-infinity, which equals any number. because

 

infinity-infinity-3 is absorbed in infinity like a blackhole. and still equals infinity-infinity, likewise infinity-infinity-5 equals the same thing.

[MWresearch]

What?

[Robittybob1]

The answer is yes!

 

infinity*0= infinity (1-1)=infinity-infinity, which equals any number. because

 

infinity-infinity-3 is absorbed in infinity like a blackhole. and still equals infinity-infinity, likewise infinity-infinity-5 equals the same thing.

Is Infinity - 99.9% of infinity still infinite?

Edited March 7, 2015 by Robittybob1

[John]

Keep in mind that my response here is in the context of the real numbers with addition and multiplication defined in the usual way.

The answer is yes!

infinity*0= infinity (1-1)=infinity-infinity, which equals any number. because

infinity-infinity-3 is absorbed in infinity like a blackhole. and still equals infinity-infinity, likewise infinity-infinity-5 equals the same thing.

The answer is yes, but not for the reason you claim.

Infinity is not a number, and thus arithmetic statements containing infinity, like [math]\infty - \infty[/math], aren't valid.

Rather, something like [math]0 \times \infty[/math] comes up in the context of some limiting process. The "indeterminate" aspect can be thought of as arising because we can take different "paths" towards [math]0 \times \infty[/math] depending on the limit in question, and arrive at different results.

Consider, for example, the following four limits, which all approach [math]0 \times \infty[/math] in the limit:

 

1. [math]\lim_{x \to \infty}0 \times x = 0[/math]

2. [math]\lim_{x \to \infty}\frac{1}{x} \times x = 1[/math]

3. [math]\lim_{x \to \infty}\frac{1}{2x} \times x = \frac{1}{2}[/math]

4. [math]\lim_{x \to \infty}\frac{1}{x} \times x^2 = \infty[/math]

Is Infinity - 99.9% of infinity still infinite?

"99.9% of infinity" isn't really valid, but if it were, then yes.