this doesn't make sense to me, smart people? (infinity)

[surviva316]

Or another way of putting it is you're saying that

infinitelyxinfinity > Axinfinity > infinity (where A>1)

And I'm saying they're all equal.

What happens when you divide each of those terms by infinity?

If you say that it becomes infinity > A > 1, then you have proven that the greater than relationship you presented in fact correct, in which case not all infinites are equal.

If you say that you cannot assume that, then you are saying that infinity/infinity is not necessarily 1, but all equivalent values DO necessarily equal 1 when divided by each other, so then you are saying that not all infinites are equal.

Conclusion: Not all infinites are equal, regardless of your answer to the question.

Anyway, if I'm not mistaken, infinityXinfinity > Ainfinity > infinity is a false assumption. I think that 2(inf) can be "less than" just infinity (I realize I'm playing really fast and loose with the terminology from a mathematical standpoint). Infinity's too general of a term to know for sure. To use the Christian analogy, that would mean that two human Christian souls > God Himself.

I'll jump in from a more conceptual, non-mathematically, possibly flawed perspective and see if I can help. Let's imagine that we referred to all very big numbers (like anything greater 12,736) as simply "more than I can be fucked to count." So how many grains of sand are on the beach? More than I can be fucked to count, I'll tell you that much. How many USD is the US in debt? Again, more than I can be fucked to count. Are there more grains of sand on the beach than there are dollars that the US is in debt? Obviously the correct answer here is "I don't know."

Obviously if you subtract some number that is more than I can be fucked to count from the US debt, then it is more likely that this will leave more room in the debt or actually make for a surplus than it will make the debt exactly zero, because "more than I can be fucked to count" is just an entire massive class of numbers, most of which are not equivalent.

I'm sure it's not a perfect mathematical analogy, but it might be conceptually helpful to the idea of infinity. It's just anything that isn't finite; that doesn't mean that they're all some number that's just the greatest number ever wrought (in fact, it most definitely does NOT ever mean that). Some non-finite amount of something can (and most likely are) be different from another random non-finite amount of something else.

[Savy]

What happens when you divide each of those terms by infinity?

Remember when I said that infinity isn't a number it was a concept and you didn't really seem to take my post seriously.

Well, that question is similar to asking what happens when we divide 8 by potato.

Also I do believe the real and natural number sets have cardinality, its just complicated to demonstrate.

Eg. You give me 0.1, I give you 1, you give me 0.2, u give you 2. Now you yet to get clever and give me 0.15, I give you 3. You give me 0.15789, I give you 4. You can go on to infinity, interestingly enough, so can I.

That's wrong, and someone has already posted the logic behind why it is wrong.

The reason in easier logic (but by no means anywhere near a proof, as I am just looking at positive real numbers) is that the natural numbers are countable.

1, 2, 3, 4, 5, 6, 7.....

Whereas to count the real numbers no matter what number you pick we get more, so much so that they aren't countable.

0.1, 0.2, ohh wait we can also have 0.15 and loads of others numbers, let's try 0.01.

0.01, 0.02, ohh wait we can also have 0.015 and loads of other numbers, let's try 0.001

0.001, 0.002, ohh wait ...

As the real numbers are uncountable, that makes them a bigger set. Therefore there is no amount of natural numbers we can use to match up them all, as we could always find a real number in between ANY two real numbers, whereas we can not find a natural number in between ANY two real numbers because natural numbers next to each other, i.e. 1&2, 8&9, 214124&214125 don't have another natural number between them.

[rong]

As the real numbers are uncountable, that makes them a bigger set. Therefore there is no amount of natural numbers we can use to match up them all, as we could always find a real number in between ANY two real numbers, whereas we can not find a natural number in between ANY two real numbers because natural numbers next to each other, i.e. 1&2, 8&9, 214124&214125 don't have another natural number between them.

The bold part, no amount of natural numbers is correct, but an infinite amount, well now we can.

[surviva316]

Remember when I said that infinity isn't a number it was a concept and you didn't really seem to take my post seriously.

Well, that question is similar to asking what happens when we divide 8 by potato.

I wasn't not taking it seriously; I was agreeing. The passage you quoted when you said "infinity isn't a number, it's a concept" said almost the exact same thing except in different words.

The passage you quoted was me using a hypothetical to disprove that infinites are equivalent. I said later in the post that the whole exercise was irrelevant and impossible. The point was that given rong's premise (that infinites are an amount, all of which are equivalent to each other), then any amount that is divided by an equivalent is 1, which would disprove rong's own point.

Again, though, later in the post I went on to say that the premise is wrong anyway and all of the terms couldn't be compared because infinity isn't a number.