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

[givememyleg]

another dumb guy here, i think that's good analysis.

in a way it sounds like he's saying one set of infinity is larger than the other? but that sounds impossible, (infinity) = (infinity * 100) or whatever you want. infinity is even the same as infinity * infinity.

[spoonitnow]

another dumb guy here, i think that's good analysis.

in a way it sounds like he's saying one set of infinity is larger than the other? but that sounds impossible, (infinity) = (infinity * 100) or whatever you want. infinity is even the same as infinity * infinity.

Some infinities are larger than others. They're considered to be different numbers. What's fun is that you can prove that some infinities are different from each other without being able to prove which one is larger.

The easiest place to start to wrap your head around it is getting an idea between what's countably infinite and uncountably infinite. The natural numbers {1, 2, 3....} are countably infinite, and all of the reals between 0 and 1 are uncountably infinite. You can prove that these two sets have different sizes with a little bit of logic. Without getting too deep into the math:

Step 1: Assume that they have the same size.
Step 2: Do some shit.
Step 3: You get a massive contradiction that proves the assumption in step 1 is false.

I'm pretty sure the details of step 2 are covered in first-level real analysis classes, though you might be able to find an easy-to-digest version online somewhere.

[a500lbgorilla]

Describe infinity.

You'll never run out of ways to describe it because the concept is a symptom of inherent human reasoning.

It's a symptom of mathematical reasoning through induction. If you say 0 exists, and you say 1 exists, and you say 1 is the immediate successor of 0, then you're allowed to say there is an immediate successor to the immediate successor of 0.

It's inherent to the concept of recursion which underlies human thought. Any time you construct a thought that places an object in a setting, you're nesting one thought inside another thought.

Or the recursion of placing the idea of a successor to 0 inside the idea of a successor to 0.

0=0
1=1=0+1
2=1+1=(0+1)+(0+1) = (0+(0+1))+(0+(0+1))
3=2+1=1+1+1=...
.
.
.

It's a symptom of human thought that when you try to formalize it or describe it, infinities keep popping up. Because in our minds, we have no trouble seeing that because 0 and 1 exist and their relation is defined, 100 exists, 1000 exists, 1000000000000000000000000...0000 exists.

And that's why people who try to describe reality don't like it when infinities pop up because it's a sign that our thinking is getting in the way.

[MadMojoMonkey]

If you say 0 exists, and you say 1 exists, and you say 1 is the immediate successor of 0, then you're allowed to say there is an immediate successor to the immediate successor of 0.

I smell a degree in mathematics.

That sentence is, at its core, the foundation of all math.

I mean, historically, it was the postulate of 1, and the successor was 2 (It was 100 years later that someone "discovered" the number 0), but the successor function was the first mathematical idea.

So it probably confuses us for the same reason that it confuses us that 1/3 is 0.3333... and 3/3 is 0.999... and 0.999... = 1 because it's not like it's forever trying to get to 1, it's actually just 1.

Actually, all of the rational numbers are dually stated. for example, 0.299999 (repeating 9) = 0.3 ; .012319999 (repeating 9) = .01232.

Every number has (at least) 2 names.

*note, this is not an artifact of the decimal system, in any base, this phenomenon exists.

[Lukie]

.999... = 1

true or false.