Infinity is a concept. So trying to multiply 0 by infinity is a lot like making this multiplication literally with a programming language (of course, a lot like, but not exactly like). You could usually safely declare 0 as int, but what would you declare infinity as? The very nature of its inability to be accounted for prevents it from being declared as int.
(√-1) || (i) is an imaginary number, and a concept, and has a very real application.
For the below, I'm going to space it a bit:
One tangible example would be the calculation of the probability of near-Earth object hitting Earth causing the end of the world as we know it.
We know that it will be a number of extreme smallness
(i.e., the probability of one near-Earth object hitting Earth)
multiplied by a number of extreme largeness
(i.e., the number of near-Earth objects for years to come).
And the result? -- we really do not know, until we know it for sure.
I don't see that as a good example. Simply because of the fact that while you do have some amount of knowledge in the number of near earth objects, nobody can truly know the number. Therefore, any calculation is subject to change.
In my mind, that's similar to calculating your risk of getting hit by a drunk driver. You can calculate the number of cars on a given route, factor in the number of drunk driving incidents reported in your route in a given time period and produce a probability of getting creamed on your way to work.
It only takes on drunk a-s-o-e to ruin all of your calculations.
Maybe I took that one wrong?
Another tangible example would be the measurement of something extremely light with an electronic scale. Each of the extremely light item would read as having the mass of 0 on the scale. And there really isn't any way to know if it really has 0 mass or it is just very light. But as we duplicate this extremely light item, which is infinitely small from the electronic scale's point of view, i.e., it is unable to comprehend or process how small it is, to the infinite amount of items, then there might be a comprehensible result -- or not -- we do not know, until we know it.
I think I get where you're going, but I don't agree that it's applicable. Simply because your use of the term "infinitely small" doesn't really represent the true meaning of infinity... endlessness. At some point, you can measure the size of the "infinitely small" particle/resonating string/etc. There is a limit there and the use of the word "infinitely" is somewhat of an oxymoron when combined with a term describing a relational size.
#BlownOutOfProportion . . . .
Negative. I have become quite entertained with the unknowable debate here. As I'm sure that Dale would agree too.
Meanwhile in the real world...
1/0
yes/no
on/off
true/false
When you add/subtract/multiply/divide by 0 you will still have the number you were trying to carry out those functions on. 0 is nothing to start with, in abstract or the real world.
What
real world would that be? The world we live in only exists in the way we believe it to...
Quantum superposition is a fundamental principle of quantum mechanics. It holds that a physical system—such as an electron—exists partly in all its particular, theoretically possible states (or, configuration of its properties) simultaneously; but, when measured, it gives a result corresponding to only one of the possible configurations (as described in interpretation of quantum mechanics).
So hypothetically; how many times could someone not give me something? Think about the potential there; at any given time they could, so the number of times that pass that they didn't give that item to me is infinite, assuming that I lived for an infinite amount of time.
Consider that everything in the universe is infinite. Nothing dies, everything simply changes.
Particles are constantly assembled and destroyed in the vacuum of space. As energy meets it forms matter, and then returns to energy as the particle deteriorates. The energy is never 'lost' or 'destroyed', it simply moves on to the next meeting place.
Back to my point, infinity is very real as the energy all around us is infinite, it has no end in the form of energy, only changes in its state of existence.
And in closing:
I just want to point out that I find this discussion very enticing.
[...]
It really is getting (and probably has to be) philosophical, which is great fun.
Agreed.
