Skeptical Dude wrote:
Infinity is undefined or indeterminate, so what's the difference?

Don't be offended, but do you know arithmetic?

As I have concluded, Infinity is not a quantity. As you have concluded, 1/0 is not a quantity. Because 1/0 is not a quantity, we can represent it by it's opposite, 0/1

I just made a whole lot of point there.

Skeptical Dude wrote:
As I have concluded, Infinity is not a quantity. As you have concluded, 1/0 is not a quantity. Because 1/0 is not a quantity, we can represent it by it's opposite, 0/1

I just made a whole lot of point there.

I didn't conclude that 1/0 is not a quantity. But even if I had, that doesn't imply that 1/0 = 0/1. That's a violation of the rules for division/fractions.

The point is that if you divide X by N, then the result A should be able to be multiplied by N to get X. For instance, 9/2 = 4.5, and 4.5(2) = 9. But if you divide, say, 5 by 0, and assert that the result is 0, then you're implying that 0(0) = 5. But actually no A works out for 5/0 inasmuch as they all have to multiplied by 0 in order to get to 5, but anything multiplied by 0 = 0. Ditto even if we're not dividing 5 by 0.

Now the only exception to the above is the case of zero divided by itself. Here, any number we give as the result of dividing by zero could, if multiplied by zero, equal 0. For instance, let 0/0 = 12. Well, since 12(0) = 0, that's okay. But doesn't 39(0) = 0, too? So if we said that 0/0 = 39, that'd also be okay. But now consider that any number as the result of dividing zero by itself would work—4, 8, 15, 16, 23, 42, you name it, when multiplied by zero, it equals zero.

Because N/0 has no possible evaluation when N does not = 0, we say that for N not equal to 0, the expression N/0 is undefined. But because when N = 0, we have an infinity of possible evaluations, we instead call the evaluation of 0/0 indeterminate.

There's another way to explain the above in terms of multiplication/division being iterated addition/subtraction, but I'll set that aside for now.

Hope this helps.

But if you divide, say, 5 by 0, and assert that the result is 0, then you're implying that 0(0) = 5

Exactly, I was trying to explain that logic completely changes when you need to use a system which we think applies "infinity". My whole point in this topic was to explain how it all ends up at representing things where we can only define everything other than concrete expressions with opposites, which are concrete expressions. Let me give an example:

Where void space = 0 and filled space = 1, we would need an infinite number of 0's (because space is infinite). However, we only need a single 1 and the space will be existant. Why? because 0 + 1 = 1. An independant thing, ( or as in this case, a 0 ) is nothing.

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Oh yeah, and the system of logic that evolves from infinity depends on what you are applying it for.